The Robins cruised to victory over Peterborough United, after their fellow relegation battlers had been reduced to 10 men early in the first half.
Paul Anderson broke the deadlock on five minutes when he found the net with a diving header from close range following a good cross from Baldock.
Lee Tomlin was shown a straight red card seven minutes later for an alleged elbow on Greg Cunningham.
Posh responded well to losing Tomlin and they levelled the scores on 19 minutes when Grant McCann coolly converted from the penalty spot, after Tom Heaton had been penalised for a foul on George Boyd.
However, City regained the upper hand and restored their lead with eight minutes of the opening period remaining.
Anderson found Baldock with a clever through ball and the former West Ham United forward beat Robert Olejnik with a cheeky lob.
City utterly dominated the second period, adding two more goals to their tally.
Baldock then notched his second of the game four minutes later with an emphatic penalty kick, after Anderson had been felled by Micheal Bostwick.
City, who started the day at the bottom of the Championship table, have moved above Peterborough into 22nd place.
Both sides are now three points from safety.