The Black Cats were not helped by the fourth-minute dismissal of Wes Brown for a professional foul on Long, who then compounded Sunderland's misery by opening the scoring on 16 minutes.
The incident severely dented Sunderland's aspirations and it was no surprise when Hull doubled their lead in the second half through Jelavic, his first for the Tigers.
Arsenal's capitulation at Liverpool and Manchester City managing only a draw at Norwich opened the door for Chelsea to go top of the table on Saturday night.
And Eden Hazard's hat-trick ensured the "little horse", as Jose Mourinho described his team after victory at Manchester City, took full advantage.
Premier League
1 Chelsea 56
2 Arsenal 55
3 Man City 54
4 Liverpool 50
5 Everton 45
6 Tottenham 44
7 Man Utd 40
8 Newcastle 37
9 Southampton 36
10 Swansea 27
11 Hull City 27
12 A Villa 27
13 Stoke City 26
14 C Palace 26
15 West Ham 25
16 Norwich 25
17 Sunderland 24
18 West Brom 23
19 Cardiff 21
20 Fulham 19
With erstwhile leaders Arsenal sinking to a miserable 5-1 loss at Liverpool in the lunchtime kick-off and City held 0-0 at Norwich, Chelsea moved a point clear at the top of the pile courtesy of a comfortable 3-0 win over Newcastle at Stamford Bridge.
Hazard, this week dubbed the best young player in the world by his manager, went a long way to living up to that billing as he swept home a fine opener from the edge of the box on 27 minutes
The Belgian made it two on 34 minutes, converting smartly after a superb one-two in the area with Samuel Eto'o. The former Lille playmaker celebrated his treble in the second half, converting from the spot after Mapou Yanga-Mbiwa brought down Eto'o.
While Chelsea appear to be hitting their straps in the title race, the opposite is true of Manuel Pellegrini's City.
After Monday's damaging 1-0 defeat at home to Chelsea, City were expected to get back to their free-scoring ways at Carrow Road but came up short as Chris Hughton's hosts earned a notable shut-out.
City's woes were nothing compared to those of Arsenal, however, who shipped four goals in the opening 20 minutes against a rampant Liverpool.
Martin Skrtel hit a brace inside the opening 10 minutes for Brendan Rodgers' men, while Raheem Sterling also claimed a brace of his own either side of Daniel Sturridge's strike as Liverpool hit five against the Gunners in the league for the first time since 1964.
Away from the title battle, the action was just as heated at the foot of the table with Swansea, Crystal Palace, West Ham and Hull each claiming key wins in their fight to beat the drop.
In the evening kick-off, Garry Monk's audition to become Swansea's next manager got off to the perfect start with a handsome 3-0 victory over local rivals Cardiff in a frenetic south Wales derby.
Monk, installed as head coach following Michael Laudrup's dismissal, watched Wayne Routledge give his side the lead just after the break before Nathan Dyer and Wilfried Bony secured the bragging rights late on.
Kenwyne Jones missed two excellent first-half chances while the superb Craig Bellamy rattled the crossbar for the visitors.
Premier League
Swansea 3 - 0 Cardiff
C Palace 3 - 1 West Brom
A Villa 0 - 2 West Ham
Norwich 0 - 0 Man City
Southampto 2 - 2 Stoke City
Sunderland 0 - 2 Hull City
Chelsea 3 - 0 Newcastle
Liverpool 5 - 1 Arsenal
Earlier, no fewer than three debutants were on the scoresheet as Palace ran out 3-1 winners at home to West Brom, who now find themselves inside the bottom three.
Tom Ince, signed from Blackpool on deadline day, marked his Eagles bow with a goal after 15 minutes, while Joe Ledley, freshly arrived from Celtic, made it two just before the half-hour.
Another debutant on show needed just 60 seconds to announce his arrival in English football as West Brom's Thievy Bifouma, on loan from Espanyol, scored after entering the action as a half-time substitute.
Palace made the points safe in the 69th minute when Marouane Chamakh won and scored their third from the penalty spot, although there was more than a little doubt over the award of the spot-kick, with Baggies goalkeeper Ben Foster appearing to connect with the ball as he challenged the Moroccan.
Sam Allardyce's West Ham set aside the controversy over their failed bid to overturn Andy Carroll's recent red card as they claimed an eye-catching 2-0 win at Aston Villa.
Kevin Nolan scored twice for the visitors, the first coming within a minute of the restart and the second just two minutes later as West Ham moved out of the relegation zone.
In the day's other game, at St Mary's, Southampton and Stoke played out an entertaining 2-2 draw.
A Rickie Lambert free-kick put the Saints into the lead but Stoke pulled level seven minutes before the break through Peter Odemwingie.
The hosts immediately restored their advantage as Steven Davis fired home, but the Potters levelled a second time through Saints old boy Peter Crouch.