The defender, signed from Morecambe in 2018, lit up a dull first-half in the 36th minute when he opened the scoring with a brilliantly-taken volley.
The fifth-placed visitors huffed and puffed after the break but Brian Rice’s side pulled out all the stops to keep their goal intact for the win that moved them six points clear of second-bottom Dundee, who play Celtic at Dens Park on Sunday.
The international break gives both managers time to gather their thoughts but it will be Rice rather than Craig Levein who will enjoy it the most after this hard-fought encounter.
Rice had been fuming after last week’s 3-0 defeat to Lanarkshire rivals Motherwell but he made only one change with McGowan back in the side at the expense of Delphin Tshiembe and how important a change that turned out be for the home side.
Levein, whose side had made it into the semi-finals of the William Hill Scottish Cup on Tuesday night with a replay win over Partick Thistle, made four changes with David Vanecek, Jamie Brandon, Peter Haring, and Callumn Morrison reinstated.
A sodden artificial surface made the ball zip around at speed as both sides battled to establish some sort of early authority.
Tony Andreu and Mickel Miller both had efforts which failed to really trouble Jambos keeper Zdenek Zlamal.
For Hearts, Morrison’s powerful left-footed shot from 25 yards flew just wide, giving the visiting fans a moment of much-needed excitement.
In the 32nd minute McGowan’s header from Andreu’s corner was clutched safely by Zlamal but that was soon followed by a moment of magic from the 22-year-old Englishman.
When fellow defender Lenny Sowah slung in a cross from the left McGowan adjusted his body to hook the ball high past the helpless Zlamal from 14 yards.
That set-back sparked the Edinburgh men into life.
Vanecek rattled the bar with a shot and Arnaud Djoum’s header on the rebound was cleared for a corner by Hamilton defender Alex Gogic, but the home side survived.
The powerful Uche Ikpeazu replaced Vanecek for the start of the second half with another attacker, Aidan Keena, on for Mulraney 10 minutes later when there appeared to be no discernible improvement.
In the 66th minute, with Accies battling ferociously to hold on to their lead, Levein made his final substitution with Harry Cochrane replacing Brandon.
However, still the Gorgie side struggled to create anything clear cut.
A drive from Keena sped high and wide before Ikpeazu headed a Morrison cross over the bar, with Hamilton seeing out an inevitable late surge from the Gorgie men.