Despite falling behind to a Dale Carrick effort midway through the first half at Forthbank, the Citizens provided the perfect response as John Robertson's penalty seven minutes before the half-time interval, and an Innes Murray strike 11 minutes from time, secured a precious three points for the visitors.
The Binos, who have now lost three league games in a row, also had Ray Grant sent off for a second bookable offence.
Saturday's victory followed up last Friday night's 3-1 win over Stranraer and provided further evidence the Capital side have put the recent embarrassing 4-0 defeat to Albion Rovers firmly behind them.
City are fifth in the League Two standings but level on points with Annan, who are fourth by the virtue of a superior goal difference.
However, City could move up to third with victory in tomorrow night's rearranged fixture with Elgin City at Borough Briggs.
Former Hearts and Livingston striker Carrick had given Kevin Rutkiewicz's men the lead when he converted a Kieran Moore cross from the right.
Ouzy See then went down under a challenge in the box and Robertson remained composed to restore parity from 12 yards.
And City capitalised on their numerical advantage following Grant's dismissal when Murray's astute finish found the bottom corner in the 79th minute.
Manager Gary Naysmith has been hugely encouraged by his players' response to the Albion loss just over a fortnight ago.
He said: "After the disappointing result and performance against Albion Rovers, the players have responded brilliantly and we now look to continue that going into Tuesday night's game at Elgin.
"Although Elgin are currently at the wrong end of the table, we know we face a difficult game. The added incentive for us though is that we know three points would take us into third in the table.
"It is also good to see the squad is looking stronger and this is maybe something that I might look to use tomorrow night."