Their prospects of upstaging the highly-fancied visitors suffered a first major setback inside three minutes when referee Andrew Kitchen wasted no time showing Hamer a straight red card for his badly timed two-footed tackle on Veltman.
Despite that, a bombardment of long throws and set-piece deliveries from the Imps – as well as an attacking energy charged by the atmosphere of the occasion – had West ham pressed back at times despite being up against 10 men.
But a heavy touch from McGrandles was pounced on by Bowen, and the defender’s inexplicable decision to pull the West Ham captain down as he was about to break free on goal, changed all that.
Now two men short, any grip Lincoln had on the game was gone and they could only boast 19% possession by the time Mavropanos’ towering header put the Hammers 1-0 up in the 45th minute.
Austbo came off the bench to make it two with the pick of the night’s goals, cutting in from the left before bending the ball into the top corner from the edge of the box.
Bowen then drove at the Imps from the right just moments later, skipping inside before beating Lincoln goalkeeper George Wickens at his near post with a low shot, and when Pablo crashed home his header to make it 4-0, Lincoln supporters began streaming out of the ground.
Soucek then showed great control in the box to score his first goal since West Ham beat Everton in the Premier League in April, before capping a terrific night for the Hammers by pouncing for their sixth in the 89th minute when Wickens spilled the ball in the box.