The former Bayern Munich marksman, who overturned a three-goal deficit with a hat-trick in the eight-goal thriller at the JJB Stadium back in December, netted a headed double as ten-man Rovers moved to within a point of sixth-placed Portsmouth.
Santa Cruz opened the scoring on 11 minutes, before a Marlon King penalty restored parity after Chris Samba was shown a straight red card for a foul on Emile Heskey inside the box.
Former Wigan striker Jason Roberts raced clear to add Rovers' second on the stroke of half-time, before Santa Cruz completed the scoring midway through the second half.
And a miserable day for Wigan was complete when Wilson Palacios picked up his second yellow card of the game.
With just a couple of minutes on the clock, goalkeeper Chris Kirkland landed awkwardly after claiming a high cross and following a lengthy period of treatment, David Bentley looked to put him under immediate pressure.
On nine minutes, the England midfielder's long-range strike had to be palmed around the post and just two minutes later Rovers took the lead.
Bentley's swerving strike from fully 30 yards was too hot to handle for Kirkland and Santa Cruz arrived on cue to head home the rebound from close range.
But the talking point of the game came just five minutes later. Heskey found himself clean through on goal following a poor backward header from Andre Ooijer and the former Liverpool forward was sent tumbling to the ground under minimal contact from the retreating Samba.
Referee Mike Dean wasted little time in first pointing to the spot and then brandishing the red card, before King coolly stepped up to slot home.
King almost doubled his tally with a confident curler two minutes later, before Rovers again began to dominate.
At the midway point of the half, Santa Cruz's crisp strike was well kept out by Kirkland after Roberts had tried to bundle his way into the box and, a quarter of an hour later, Bentley's brilliant free-kick struck the stanchion after David Dunn's run had been brought to a halt on the edge of the box.
Roberts' goalbound header on 38 minutes was then blocked by Erik Edman, who appeared to pick up a serious injury in the process, but on the stroke of half-time, the Grenada international did restore Rovers' lead.
Stephen Warnock's long ball forward was flicked on by Santa Cruz and after turning Emmerson Boyce inside out, Roberts fired a low left-foot strike through Kirkland's legs and into the empty net.
Rovers had penalty appeals of their own eight minutes after the break when Bentley picked out Santa Cruz with an inch-perfect ball over the top, but Mario Melchiot just got back to make a goal-saving tackle.
Santa Cruz ought to have done better from Morten Gamst Pedersen's centre just past the hour mark, but just two minutes later and the Paraguayan did strike again. Zurab Khizanishvili made a vital interception, before sending Bentley down the left, the England man bided his time before floating over a cross to the far post, where Santa Cruz was waiting to head home.
Michael Brown stung the gloves of Brad Friedel with a well-struck shot from distance, before the visitors' task was made doubly difficult when Palacios picked up his second booking of the afternoon for mistimed tackle on Dunn.
Both sides pushed for further goals, but Rovers saw the game out comfortably to signal a return to winning ways.