Leading 1-0, the Reds were rocked in stoppage-time when the Sky Blues, dominant for swathes of the game after going behind to Dominik Frieser’s 39th-minute strike, were controversially awarded a spot-kick.
It came after Jordan Williams challenged Jamie Allen, with the penalty awarded on the call of an assistant after referee John Busby did not initially penalise the tackle.
But the fateful hand was played by Collins, who saved Gyokeres’ spot-kick on a day when the hosts received eight yellow cards.
He said: “I was just trying to psyche him out a bit and shout a bit longer.
“I read him and thought he’d go for his favoured side, which was my right and I managed to get down low and save it and get the rebound.
“You always want your first clean sheet on the board nice and early and in the second game, we have got it.
“But we’ve a lot to improve on and I’m sure we will do.”
The game was settled by Frieser, who coolly slotted home after being played in by the excellent Romal Palmer. It was the Austrian’s first strike on home soil after failing to find the net on at Oakwell last term as head coach Markus Schopp was left to savour a winning start at Oakwell.
Frieser said: “I am very happy. It’s my first goal at Oakwell and the first time I have scored in front of Barnsley fans and I have been training hard for this.
“It was a moment I will never forget. I was so happy running to the fans, I was searching for my wife but I could not find her!”
The only downer saw key striker Carlton Morris exit the fray in the first half.
He watched the second half from the West Stand and was wearing a leg brace, with the Reds anxiously awaiting scan results.
Barnsley: Collins; Sibbick, Helik, Kitching; Brittain, Styles, Palmer (Benson 63), B Williams (J Williams 69); Morris (Oduor 33), Frieser, Woodrow. Unused substitutes: Walton, Moon, Halme, Adeboyejo.
Coventry: Moore; Hyam, McFadzean, Rose (Clarke-Salter 77); Dabo, Hamer, Sheaf (Allen 77), Maatsen; O’Hare; Gyokeres, Walker (Waghorn 17). Unusued substitutes: Jones, Wilson, Shipley, Da Costa.
Referee: John Busby (Oxfordshire).