The game looked destined to end in a draw when Watt fastened on to Scott Tanser’s cross to head past Dean Lyness from close range.
St Mirren’s best chance had come from Paul McGinn midway through the second half, while St Johnstone substitute Chris Kane shot wide from a matter of yards minutes before Watt spared his team-mate’s blushes with his late header.
The hosts made two changes from the side which defeated Motherwell on Saturday, with Adam Hammill and Cammy Smith replacing Cody Cooke and Ryan Edwards.
St Johnstone also made two changes after their home loss to Rangers. In came Watt and Danny Swanson, replacing David Wotherspoon and Ross Callachan who were both named as substitutes.
Callachan, however, would be called into action after just 16 minutes to replace Murray Davidson who suffered an injury following a collision with Stephen McGinn and could not continue.
That disruption did nothing to help a first half that failed to throw up a single shot on target for either side. It took until the 42nd minute for an effort of any consequence, a Hammill drive that went well wide.
The quality of football was marginally better in the second half. St Mirren defender Alfie Jones was a relieved man to see Callachan shoot wide after hitting his clearance straight to him, before the former Hearts midfielder was booked for simulation just a minute later after tumbling in the St Mirren box.
The home side then enjoyed some sustained pressure but could not convert it into a goal. Lee Hodson had a tame lofted shot that was easily held by Zander Clark, before Paul McGinn reached Ethan Erhahon’s cross at the back post but saw his shot blocked by Callachan.
St Mirren kept probing away and Smith saw a deflected shot loop over for a corner, while at the other end Richard Foster’s thumping drive was touched over by Lyness, before the goalkeeper similarly denied Tanser.
Kane had a great chance to win it six minutes from time but shot wide from Jason Kerr’s knock down before Watt sealed the win late on.