The Togo international striker turned in a fine individual display as Spurs tore Alan Pardew's depleted side to shreds at St James' Park to maintain the pressure on the top four with a 4-0 rout.
He struck from close range with just 19 minutes gone on a wintry Tyneside night to give the visitors a lead they never looked like relinquishing, and Aaron Lennon was only denied a second by the post.
The game was effectively over eight minutes into the second half when Paulinho was presented with an equally straightforward task to double his side's lead after goalkeeper Tim Krul failed to hold Adebayor's stinging shot.
Adebayor doubled his tally with seven minutes remaining when the unfortunate Krul made a good save to deny substitute Andros Townsend, but saw the frontman follow up to complete the scoring.
Tottenham were not finished, however, and the Dutchman found himself picking the ball out of his net for the final time five minutes later after being beaten from distance by substitute Nacer Chadli.
Tim Sherwood's men were simply too pacy, too inventive and too clinical for their hosts, who could not match them in any department.
The win took Spurs' points tally to seven from a possible nine since their 5-1 humbling by Manchester City and kept them firmly in the race for Champions League qualification.
But for Pardew, it proved a miserable way to celebrate 150 games at the helm and provided further evidence that, despite his denials, the club has little more than pride for which to play for the remainder of the season.
It was the first game at St James' since a second successive 3-0 derby defeat against Sunderland and neither the performance nor the result went down well with the home fans among a crowd of 48,264 who have now seen their side claim just four of the last 24 points they have contested.
That, coupled with simmering resentment over owner Mike Ashley's decision to sell and not replace Yohan Cabaye last month, made for an ugly atmosphere, and one which is unlikely to improve in the short term if things do not improve markedly on the pitch.
Premier League
1 Chelsea 57
2 Arsenal 56
3 Man City 54
4 Liverpool 53
5 Tottenham 50
6 Everton 45
7 Man Utd 42
8 Southampton 39
9 Newcastle 37
10 Swansea 28
11 West Ham 28
12 A Villa 28
13 Hull City 27
14 Stoke City 27
15 C Palace 26
16 Norwich 25
17 West Brom 24
18 Sunderland 24
19 Cardiff 22
20 Fulham 20
Arsenal were denied a return to top spot in the Barclays Premier League after Manchester United battled to a goalless draw at the Emirates Stadium.
Chances were at a premium between the two sides, with the best coming in the opening minutes as former Arsenal captain Robin van Persie, now in the United camp, and home striker Olivier Giroud should both have scored.
Arsenal goalkeeper Wojciech Szczesny pushed a bullet header from the Holland forward against the crossbar in the second half of a match which ultimately failed to live up to its billing, leaving Jose Mourinho's Chelsea still top of the league.
David Moyes' visitors were almost gifted a lead inside the first minute when Mikel Arteta gave the ball away to Van Persie, but the one-time Arsenal skipper saw his scuffed shot saved.
French forward Giroud headed an Arsenal corner wide from inside the six-yard box in what was an electric start.
However, the tempo of the match then dropped, with only a deflected effort from Tomas Rosicky causing United goalkeeper David De Gea some concern during the lull.
United - looking to make up ground on the top four following their 2-2 draw at home with Fulham - continued to frustrate Arsenal with a determined midfield display, closing down space quickly when not on the ball.
When Arsenal did get into second gear as the hour passed, Antonio Valencia cleared a header off the line from Arsenal defender Laurent Koscielny.
Giroud just could not get on the end of a great cross from right-back Bacary Sagna before, at the other end, Szczesny tipped a bullet header from Van Persie against the frame of the goal.
De Gea twice saved from Santi Cazorla during the closing stages as Arsenal pressed for a winner, but each team had to be content with a point.
Steven Gerrard secured Liverpool an incredible 3-2 stoppage-time victory at Craven Cottage, rifling home from the penalty spot to break struggling Fulham's hearts.
The visitors' six-match unbeaten league run looked in serious danger of ending on several occasions in west London as Rene Meulensteen's side produced a performance that belied their position at the bottom of the table, only for them to twice see leads pegged back before Gerrard's late goal.
It was a fine win but one in which Liverpool failed to get anywhere near the heady heights reached in Saturday's 5-1 mauling of Arsenal, falling behind after just eight minutes.
Kolo Toure, guilty of gifting West Brom a 1-1 draw 10 days ago, could only watch on in horror when he sliced a Kieran Richardson cross into his own goal.
Fulham continued to impress but were undone as half-time approached by a wonderful first-time Gerrard through ball, which found Daniel Sturridge to net his eighth goal since returning from injury.
While Liverpool were somewhat fortunate to go in level at half-time, they began the second half with renewed vigour and Luis Suarez rattled the far post as the Whites looked increasingly unsteady.
Fortunately for them, Martin Skrtel was looking even more shaky and his defensive mistake allowed Manchester United academy graduate Richardson to net from close range.
The lead did not last long, though, as Philippe Coutinho sent a fine shot past Maarten Stekelenburg via a slight deflection off former Everton defender John Heitinga.
Fulham looked good value to follow up their thrilling 2-2 draw at Manchester United with another point, only for Sascha Riether to foul Sturridge, allowing Gerrard to fire home a stoppage-time winner from the spot.
Swansea bad-boy Chico Flores finally made the headlines for all the right reasons as he struck an equaliser in a 1-1 draw at Stoke.
At a blustery Britannia Stadium, with the game only going ahead after two pre-match safety inspections given the storm-force winds prior to kick off, Flores deservedly earned Swansea a point as he deftly flicked home a Pablo Hernandez cross beyond the despairing reach of Asmir Begovic in the 52nd minute to keep his side in 10th place.
Arguably, Swansea should have won the game as they were the better team for the most part, aside from one spell in the first half when Peter Crouch bagged his eighth goal of the season in the 17th minute.
Crouch first teed up Peter Odemwingie for a thumping right-foot drive that crashed back off the post straight to the lanky striker whose follow-up deflected off a diving Leon Britton trying to block.
The night's other games at Manchester City and Everton were postponed on Wednesday as severe weather battered the country and endangered fans travelling to games in the north west.
Earlier on Wednesday the Met Office issued red warnings - the highest possible - for parts of Wales and north west England in the evening.
City were preparing to welcome Sunderland to the Etihad Stadium but, with just over one hour before the scheduled 1945 kick-off, the club announced the fixture would not go ahead.
Everton's home meeting with Crystal Palace was next to go, with the Merseyside club citing "building damage" around Goodison Park as the deciding factor.
Saturday February 15
FA Cup
12:45 Sunderland v Southampton
15:00 Cardiff City v Wigan Athletic
15:00 Sheff Wed v Charlton
17:15 Manchester City v Chelsea
Sunday February 16
FA Cup
13:30 Everton v Swansea City
15:00 Sheffield United v N Forest
16:00 Arsenal v Liverpool
Monday February 17
FA Cup
19:45 Brighton v Hull City