Watt netted the second goal for Tommy Wright’s 2014 cup winners, who took full advantage of goalkeeping errors by Scotland Under-21 international Ryan Fulton to stroll into the last 16.
Accies included returning midfielder Tony Andreu but there was no place in the home line-up for winger Michael O’Halloran, who had signed 24 hours earlier for a third stay at McDiarmid Park.
And Saints didn’t need him anyway. After just 45 seconds, Fulton inexplicably failed to deal with Liam Craig’s free-kick from the right and Jason Kerr’s header floated into an empty net from just six yards.
With Hamilton still reeling, home striker Chris Kane wasted two opportunities in the space of as many minutes. But a second goal arrived soon after and it was another error by Fulton.
The stand-in for injured regular keeper Gary Woods had Ross Callachan’s raking shot covered, but spilled it and Watt pounced to slam a close-range finish high into the net, prompting an angry reaction among Accies’ small band of followers.