There was little to write home about in a dour first 45 minutes.
But after the break Lewis Nyatanga’s header, from Josh Scowen’s free-kick, broke the deadlock.
Victory was confirmed when visiting goalkeeper Paul Rachubka netted an own goal.
Victory sees the Reds move five points clear of the relegation zone.
At the other end of League One, Doncaster Rovers and Bradford traded places for the remaining play-off spot.
In-form Rovers crashed to a 3-0 defeat at Port Vale.
Goals from Mark Marshall, Frederic Veseli and Byron Moore ended Doncaster’s run of three consecutive league victories.
Bradford were held to a 1-1 draw against Walsall at Valley Parade, but the point was enough to see them leapfrog Rovers.
Billy Clarke gave the Bantams the lead on 51 minutes, only for Jordy Hiwula to net the equaliser.
In League Two, York City lost 3-0 to Northampton Town at Sixfields.
Chris Hackett and Brendan Moloney put the hosts in control.
Marc Richards then had a penalty saved for the hosts after Ricky Holmes was fouled, before Ivan Toney sealed victory.
Defeat leaves the Minstermen just a point off the bottom two.