And while those last-gasp goals gave the eighth-placed Hammers their sixth consecutive victory, the beleaguered Black Cats were nudged another precarious, predictable step towards relegation.
Last season, Sunderland roared into the Premiership while West Ham had to get there the hard way, via the play-offs.
But this time around the two sides have enjoyed wildly differing fortunes.
And that was no more in evidence than during midweek when the Hammers won at Arsenal while the Championship-bound Black Cats crashed 3-0 at home to Middlesbrough.
Following their sensational 3-2 victory at Highbury, Alan Pardew made two changes as transfer window signings Ashton and Lionel Scaloni came in for joint top scorer Marlon Harewood and Clive Clarke.
Stricken Sunderland's defeat - their 18th of the campaign - at the hands of Boro led to Mick McCarthy making a quadruple reshuffle as Stephen Wright, George McCartney, Kevin Kyle and ex-Hammer Christian Bassila returned to the side.
But it was to prove a brief sojourn to the East End for his reckless right-back Wright, who was booked for body-checking the fleeing man-of-the-match Nigel Reo-Coker after just five minutes and then dismissed for tripping Matthew Etherington midway through the half.
Having seen his side comfortably steer themselves through those opening 20 minutes, that was the last thing that the furious McCarthy needed, as he was forced to withdraw the dejected Anthony Le Tallec and replace him with defender Nyron Nosworthy.
Indeed, despite coming into this game as the Premiership's fourth highest scorers West Ham failed to threaten Black Cats keeper Kelvin Davis until 39th-minute when Ashton sent a low, 18-yard bobbler goalwards.
And as the top-flight's fourth leakiest team, too, the Hammers' defence had also allowed Kyle to unleash a low, angled 15-yarder that Shaka Hislop did well to hold, while Julio Arco's cheeky chip from halfway was both high and wide.
The Wearsiders' joy at getting to the interval all-square was not shared by the East Enders, who introduced 39-year-old Teddy Sheringham in place of Zamora for the restart.
In their desperate bid to find some much needed urgency, the Argentinian Scaloni - aptly nicknamed 'The Bull' - marked his first outing in English football with a yellow card for charging into Arca, as he followed Wright, Dean Whitehead and Steven Caldwell into referee Rob Styles' notebook.
Still frustrated West Ham were failing to make their extra man count, though, and they were lucky that Kyle's shooting boots deserted him when he skied over on the hour.
Midway through the second period, Ashton finally forced a worthwhile save out of Davis when his point-blank header was acrobatically tipped over the crossbar and shortly afterwards Pardew upped the ante by thrusting Harewood into action.
That switch looked to have paid instant dividends when the substitute tapped home after Davis palmed Ashton's long-ranger into his path, but his delight was cut short by the sight of a raised offside flag.
But when the duo combined again in mirror-like fashion, with just nine minutes remaining, West Ham finally made the long-awaited breakthrough.
This time, it was Harewood who let fly with an angled shot and this time Ashton marked his debut with a simple tap-in after Davis could only divert the scorching shot into the £7million man's path.
And on 87 minutes, Konchesky sealed that sixth-consecutive victory with a low 25-yarder that squeezed through the clutches of the red-faced Sunderland goalkeeper.