League Two Wrap: Oxford end winless run
Connolly capitalised on the 74th-minute sending off of Hartlepool's Simon Walton by scoring the only goal of the game within four minutes.
Oxford now sit six points clear of eighth-placed Southend United, their next opponents, as the race for a play-off place heats up.
Chances were at a premium at the Kassam Stadium on Friday, but the hosts took advantage after Walton had seen red for a second bookable offence.
Sean Rigg was subsequently fouled on the edge of the Hartlepool penalty area and Connolly glanced David Hunt's free-kick beyond Scott Flinders.
Southend were also in action on Friday, but could only muster a 0-0 draw at Bristol Rovers, meaning Phil Brown has now seen his side fail to win in 12 league matches.
Ryan Leonard wasted the clearest opportunity of the first half, the visiting defender firing wide after being played in by Freddy Eastwood.
Rovers' best chance to win the game came just after the hour as Mark McChrystal rose unmarked at the back post but failed to put his header on target.
Lee Barnard was picked out by Leonard in the area with 15 minutes remaining, yet the forward's kneed attempt at goal was saved by Steve Mildenhall.