Natasha Flint had put the visitors in front in the first-half, but Katie Chapman’s header levelled matters before Groenen’s late intervention turned the game on its head.
Sunday's victory keeps Chelsea second in The FA WSL 1 table.
FAWSL 1 Results
Bristol Academy 1-3 Liverpool
Chelsea 2-1 Manchester City
Everton 1-2 Arsenal
Notts County 0-1 Birmingham City
“Man City had the better of the first half and it was important that we maintained our composure in the second half - but we are the home team we had to push,” said Hayes.
“I thought we had enough quality, not in terms of finishing, but in terms of chances created and quality to win the game.
"I’m delighted for Jackie who came on and made an impact and got the winner at the end, because it shows the depth and quality that we have in our squad.”
Birmingham City's Jo Potter netted the only goal of their game against Notts County to help Blues maintain their lead at the top.
Birmingham are now without a game until late August, in which time both Chelsea, who they lead by three points, and Liverpool, who they lead by five, play twice - including against each other.
“There was not a lot to choose between the teams in a tight game," said Birmingham boss David Parker.
"That little bit of quality from Jo has won it for us. This is a great win for us.
“We are working very hard as a team and are delighted to be top of the League. Chelsea have a world-class eleven and Liverpool are full-time so they will be right up there.
“We expect to come out of our break chasing them two so it will be a different mentality for us, but there is no reason why we cannot win the League.”
Action from Birmingham's win at Notts County
Arsenal, meanwhile, clinched a late win thanks to Alex Scott's 84th-minute strike against bottom side Everton.
Andy Spence's Blues are without a win this season and found themselves a goal down again when Danielle Carter put the Gunners in front.
Nikita Parris levelled for the home side before Michelle Hinnigan had a chance to give them the lead in the second half, but her penalty was saved well by Emma Byrne.
And when England defender Scott pounced to tap in, it was enough for the three points.
“It was an entertaining game but it wasn’t very entertaining for me when we conceded an equaliser in first half stoppage time. I was absolutely furious about that,” said Arsenal head coach John Bayer.
“I thought Everton were the better side for a lot of the first half. But as that half drew to a close we came on stronger and I was feeling positive about things.
“I said to the players at half time that conceding the way we did wasn’t the most professional thing. To be fair I’ve said to them afterwards that a coach wants a reaction when he gives players a ticking off.
"I got that. They were much more professional in the second half and I was delighted to see that.”
Alex Scott celebrates her Arsenal winner
In the weekend's fourth game in the top-flight, played on Saturday, champions Liverpool put in their best display of the season according to manager Matt Beard as they chalked up a comfortable 3-1 win at Bristol Academy.
Goals from Gemma Davidson, Katrin Omarsdottir and Gemma Bonner put the Reds in charge before Bristol, who had Jemma Rose sent off, grabbed a late consolation through Natasha Harding.
“That was our best performance of the season so far – I thought we were terrific,” said Beard.
“After the first ten minutes we settled down and dominated play and I was delighted with our game management. The players deserve a lot of credit.
“It has been a tough week because we have had three games in seven days and Bristol is always a tough place to come, but I thought we were fantastic."
For all the latest from The FA WSL, click here to visit the official website
