West Ham 1-0 Shrewsbury
West Ham huffed and puffed before finally blowing Shrewsbury's FA cup dreams away.
Indicative of the difficulty that the Premiership side faced was that it took 200 minutes of open play over the two ties before they managed to score.
The first real chance fell to Shrewsbury in the second half when Stefan Payne broke free, only for Joe Hart to narrow the angle and save with his feet.
West Ham then picked up the pace, with a double substitution, that saw Marko Arnautovic and Mark Noble replace the disappointing Andre Ayew and Reece Oxford.
West Ham then began to dominate, with Arnautovic seeing his fierce effort hit the side netting and then put another effort wide.
The League One side began to visibly tire as the game entered extra time, clearing two efforts off the line in the first 15 minutes.
The goal finally came in the 112th minute, with Toni Martinez scooping the ball back for the incoming Reece Burke to meet on the half volley and smash into the roof of the net.
West Ham manager David Moyes was relieved to have achieved the win.
He credited Shrewsbury for their brave performance, though felt West Ham were always stronger and more likely to score.
He confirmed that many of the changes to the side, which included youngsters Burk, Oxford, Martinez and Josh Cullen, were due to other players not being available.
Moyes also declared that he knew nothing of any £20 million bid for Andy Carroll from Chelsea or anyone else. "I want to add to the squad, not lose players." said Moyes.