Ally McCoist's men strengthened their grip on top spot in the Third Division with another away victory against the North East club, who had Rory McAllister sent off
The Ibrox side made it seven wins in a row away from home as they edge closer towards securing the title and benefitted from the sending off of Rory McAllister.
The home side made two changes from their goalless draw at Queen's Park, with David Cox and McAllister replacing Martin Bavidge and Robbie Winters.
Ally McCoist made just the one change from the side that edged a close encounter with Berwick last Saturday, as Dean Shiels was dropped to the bench to be replaced by Ian Black who returned from suspension.
Peterhead could have taken an early lead when on-loan Dundee United defender Ross Smith got in behind Ross Perry to get on the end of a free kick floated into the box, but his header was diverted behind for a corner by Rangers goalkeeper Neil Alexander.
It took until midway through the first half for Rangers to get in behind the Peterhead defence, as David Templeton raced down the left wing before cutting inside for a shot, but the winger's effort flew over the bar.
The visitors found the breakthrough on the half-hour mark when Lee Wallace burst forward into the box and Graeme Smith parried his low shot straight into the path of Sandaza, who was left with the simplest of finishes.
Jim McInally's side then had two opportunities to get back on level terms. Cox's low strike sailed wide before Ross Smith got his head to a corner from the left, but Templeton cleared off the line.
The Blue Toon started the second half well as Cox robbed Ian Black on the edge of the Rangers area and raced in from the right-hand side, but his acute-angled drive beat the crossbar.
Midway through the second half Peterhead found themselves a man down when McAllister got on the end of a long ball inside the Rangers area but failed to deal with a bounce and raised his arms to control the ball. Having already been booked, referee Mike Tumilty had no choice but to show the striker a red card.
Rangers should have secured the victory when Templeton picked up the ball in the middle of the Peterhead half before storming forward and unleashing a strike which ended up going past Graeme Smith's left-hand post.
With less than five minutes remaining Templeton had yet another chance to seal the win after being played in by a superb ball by substitute Barrie McKay, but the winger blasted his chance over.
McCoist's men continued to search for a second goal but couldn't find a way past Graeme Smith and were ultimately made to settle for a single-goal victory that sees them restore their 19-point gap over second place Queen's Park.