Championship side Argyle held out for 91 minutes at Upton Park and went close themselves on several occasions.
But England hopeful Ashton, who swapped his white boots for a bright red pair at half-time, struck late on with a superb volley for his third goal since recovering from a broken ankle.
The outcome was harsh on Argyle, who had their moments with Barry Hayles, Peter Halmosi and Akos Buzsaky all causing the Hammers' rearguard problems.
West Ham boss Alan Curbishley was finally able to give £7million summer signing Scott Parker his debut, while Freddie Ljungberg made his first start since the opening day of the season.
Parker's first touch in a claret and blue shirt was to intercept Paul Connolly's crossfield pass, and the former Charlton midfielder looked composed from the off.
Danny Gabbidon, back in the starting line-up at centre-half, got off to a jittery start with a weak backpass which forced stand-in goalkeeper Richard Wright into a hurried clearance with Ebanks-Blake bearing down on him.
Luis Boa Morte, another of Curbishley's six changes from the side beaten at Newcastle on Sunday, passed up the hosts' first chance when he collected the ball from Carlton Cole and cut inside only to shoot weakly at Luke McCormick.
Parker then linked up well with Ashton, who in turn fed Cole, but an offside flag curtailed his run on goal, before the in-form Ashton blazed a shot over as West Ham began to get a grip on proceedings.
They forced a corner in the 14th minute which Ljungberg swung straight to James Collins, whose header was cleared off the line by Halmosi at the far post.
Former Manchester United trainee Ebanks-Blake, whose only appearances for the Red Devils came in the League Cup, should have done better when sent through by Halmosi but his hurried shot sailed high and wide.
Ashton should have put the Hammers ahead in the 23rd minute when he collected Lucas Neill's pass and turned superbly on the edge of the area, but drilled his shot narrowly wide.
David Norris was too quick for the rusty Gabbidon in the 26th minute, and the Wales international's crude challenge earned him a booking.
Buzsaky, Argyle's tricky Hungarian midfielder, gave the hosts a scare with a 20-yard drive which flew inches over Wright's crossbar.
Boa Morte then missed a gilt-edged chance to fire the Hammers ahead when he played a one-two with Hayden Mullins only to dink the ball over the advancing McCormick and wide.
McCormick saved well from Ashton's first-time shot before, at the other end, Neill had to back-pedal onto the goal-line to keep out Halmosi's free-kick with his chest shortly before the break.
Cole's composure deserted him in the 54th minute when he was cleverly put through by Parker's superb chip, the striker taking a heavy touch allowing McCormick to recover his ground.
Krisztian Timar then had to clear his lines in front of goal as Ashton crossed towards Cole.
Cole appeared to be felled by a stray arm from Argyle left-back Gary Sawyer, but referee Phil Dowd took no action.
Curbishley threw on young winger Kyel Reid in place of the battered Cole just after the hour mark, with Boa Morte joining Ashton up front.
Reid had a shot deflected wide, but Upton Park was growing frustrated along with Boa Morte, who was booked for a late tackle on Halmosi.
Lee Bowyer entered the fray in the 73rd minute at the expense of the tiring Ljungberg.
The Hammers had a major let-off moments later when Neill, under pressure from Halmosi, sent an under-hit back pass to Wright.
His clearance was charged down by Hayles, but the veteran striker could not prod the ball goalwards as Neill scampered back.
Ashton then grazed the top of the crossbar with a free-kick which took a heavy deflection off the wall and spun high into the air, before Bowyer sent a volley wide.
Parker left the field in the 85th minute to be replaced by Mark Noble, while Argyle boss Ian Holloway sent on Rory Fallon for Ebanks-Blake.
Bowyer headed Reid's cross wide as the clock ticked down.
But in the 91st minute Reid sent over a low cross from the left which Ashton expertly volleyed across McCormick and into the corner of the net.
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