Arbroath boss Dick Campbell was furious his side once again missed a golden opportunity to leapfrog Forfar in the League Two title race.
A Ryan Porteous goal with the last kick of the game condemned the Lichties to a second home defeat in a row.
With Forfar losing, even a draw would have put the Gayfield men top on goal difference.
Campbell said: “We were very poor but we were 10 seconds away from being top of the league.
“My big players didn’t play today and that annoys me, disappoints me, and makes me angry. I’m not going to name them but I’ll name them on Monday night (at training).
“Edinburgh deserved to win the game because they had the best chances.
“We had all the possession, 74% if you look at the statistics, but that doesn’t mean anything unless you do something with it.
“Their centre-backs were outstanding, but I don’t remember their goalkeeper having a save to make.
“I’m sorry for the Arbroath fans but I’m not sorry for my players.
“We need to get on with it and work hard. We were 11 points behind Forfar at one stage and we could have been ahead of them now.
“But you cannot depend on anyone else. If you are going to win championships you have to do it yourself.”
Craig Beattie came close to giving City an early lead, but Ricky Gomes pushed his net-bound shot behind for a corner.
A few moments later he blocked a Joe Mbu attempt.
Until that point Arbroath had enjoyed the bulk of possession without creating many clear-cut chances, although Omar Kader and Ryan McCord both sent shots over the bar.
Lewis Allan forced a fine save out of Gomes early in the second half, then City’s Derek Riordan, shot tamely at the home keeper.
Edinburgh continued to frustrate the Lichties by getting 10 or even 11 men behind the ball, but always looked dangerous on the break. Gomes had to tip another Allan effort over the bar.
Then came the dramatic finish when Porteous bundled the ball home from close range to give Edinburgh victory.
