It has been a chaotic few days for Arsenal, who came into this match seven points adrift of City, knowing defeat would put them in a really difficult position in the WSL title race.
Pressure has been building on manager Slegers and she did not help her case when she did not show up for post-match media duties on Wednesday following their draw with Paris FC in the Women's Champions League.
Scrutiny on Slegers increased as a result, but she was calm as she addressed the situation on Friday, stating she made the decision to be with her team as they were emotional following the result.
After such a poor start to the campaign, it was perhaps understandable that City started more strongly at Etihad Stadium and were building pressure throughout the first half.
But Arsenal dug in and were rewarded for their efforts when Baum's goal was allowed to stand despite replays suggesting the forward was offside when she helped the ball over the line from Lotte Wubben-Moy's downward header.
That irked City, who responded through Hemp, and Arsenal were dealt a blow when midfielder Mariona Caldentey went off in tears with what looked like a hamstring injury just before the break.
The visitors made the brighter start to the second half though and Russo delivered a reminder of her quality when she used the space afforded to her to thump the ball into the far corner and make it 2-1.
The Gunners have struggled in front of goal this season, scoring just twice in the WSL prior to their visit to Manchester, so they looked revitalised when Russo's strike hit the back of the net.
But to lose the lead twice and come away without any points was the worst possible scenario for Arsenal, who could be out of the title race just five weeks into the season.