And that was cruel luck on Ian Holloway's side who matched their Premier League rivals blow for blow on a wet and windy night in east London.
With the Eastenders huffing and puffing to overcome the men from the West Country, Ashton changed his footwear at the break and duly broke the deadlock with a late, late winner.
Alan Curbishley may have made six changes from the side that was washed up down the Tyne at Newcastle United on Sunday, but sensing that the Carling Cup is probably the easiest route to Europe, the Hammers' boss still named a vastly experienced side.
Fit-again Scott Parker was finally given his West Ham debut following his £7million move from Newcastle in the summer, while fellow internationals, Freddie Ljungberg, Luis Boa Morte, James Collins, Danny Gabbidon and Richard Wright were also handed starts.
Without such luxuries, Holloway made only two changes from the side that had suffered its second defeat of the season at Stoke City, as he recalled Barry Hayles and top scorer Sylvain Ebanks-Blake.
Despite being 26 league places below the Eastenders, Argyle, perched in 13th-spot in the Championship, started with the sort of determination that had seen them despatch both Wycombe Wanderers and Doncaster Rovers from the competition in earlier rounds.
Indeed, West Ham struggled to get the ball out of their own half in the opening 20 minutes and, although Luke McCormick was forced to save Boa Morte's early grass-cutter, before Peter Halmosi nodded Collins' header out from under the angle, the enthusiastic Ebanks-Blake also went close with a rising 15-yarder.
Argyle's Akos Buzsaky also landed a long-ranger on the top of Wright's net and Krisztian Timar headed over, too.
But as the half wore on, West Ham started to carve out the better chances as Ashton sent a low 18-yard shot across the saturated Upton Park turf and a whisker wide of the foot of McCormick's right-hand upright, before the fleeing Boa Morte clipped the ball beyond both the advancing Argyle keeper and his left post.
And as half-time approached, Ashton's had a shot saved by the fully extended McCormick, before Hammers' skipper Lucas Neill defiantly chested Halmosi's curling 18-yard free-kick off the line to deny plucky Plymouth an interval lead.
Ashton duly emerged for the restart sporting those red boots and he quickly sent a header over the top.
But the probing Plymouth strike pairing were always a second-half threat and, on 80 minutes, only a goal-line block by the covering Neill, a split second after Wright had parried, prevented Hayles from putting Plymouth ahead.
Extra-time looked inevitable when Lee Bowyer's downward header drifted wide in the dying seconds and the soaked crowd of 25,774 were preparing themselves for another half-an-hour in the East End downpour.
But with two minutes of the allotted three additional minutes gone, those West Ham fans were soon singing in the rain as substitute Kyel Reid crossed to the back of the Argyle area, where Ashton rifled an angled 12-yard shot into the far corner to break Holloway's heart.