Even after the hosts saw Rory McAllister sent off midway through the second half, the visitors could not add to their advantage in what was an evenly-matched affair.
Missing captain Lee McCulloch through an ankle injury, the visitors made just one change to the side that had beaten Berwick Rangers handsomely last weekend, with Ian Black returning to the side in place of Dean Shiels, having completed a one-match suspension.
Spaniard Sandaza led the line, with support coming from Andy Little and David Templeton on the flanks. Peterhead made two changes with David Cox and McAllister coming in for Robbie Winters and Martin Bavidge.
And it was Peterhead who were first to threaten. Dean Cowie won a free kick in the midfield and Neil Alexander in the Rangers goal did well to turn away a Scott Ross header from Ryan Strachan's delivery. Rangers' first effort on goal saw Black seize upon Scott Ross' slack pass, to fire a snapshot from 25-yards, but his effort was always curling away from the target.
It had been a stuffy opening period, with both teams still settling into the game when Peterhead's Ryan McCann became the first player to go into the book for a cynical foul on David Templeton.
The goal then came the half-hour. Peterhead's Graeme Smith, himself a former Rangers goalkeeper, did well to save a Lee Wallace shot, but could not hold on and Sandaza reacted first to fire the ball high into the net.
Peterhead hit back, and some fine hold-up play by McAllister created an opening for Cox, but he dragged his effort wide of the post. And the Blue Toon started the second half brightly, too, as Cox squeezed out Black on the touchline and cut inside, before flashing a left-footed effort over the crossbar.
Peterhead's task was made much harder after 65 minutes when McAllister was adjudged to have handled in the area, and received a second booking, reducing his side to 10 men, while Rangers were dealt a blow themselves as Black had to be withdrawn through injury, Robbie Crawford replacing him in the midfield.
Rangers could have sealed the points with five minutes remaining. Lewis McLeod 's clever reverse pass found Templeton in acres of space on the 18-yard line, but the former Hearts man sent his effort wide of the upright.