The Spaniard netted his second goal for the Light Blues on 29 minutes and it was a poacher’s strike following excellent play from Lee Wallace.
This put Rangers on their way to an important victory against Jim McInally’s men who worked hard throughout and made the second half a battle in front of 4,855 fans.
The Blue Toon had five players booked throughout the 90 minutes, including striker Rory McAllister who was sent off after the hour mark for a second bookable offence.
Ally McCoist made one change to his team with Ian Black in the starting line-up after he served a one-match ban against Berwick last weekend.
He joined Lewis Macleod in the engine room, with Kyle Hutton dropping into a deeper role as he made his 10th consecutive start.
Andy Little featured once more on the right flank with David Templeton supporting Sandaza from the opposite side and Chris Hegarty, Ross Perry, Emilson Cribari and Wallace making up the defence.
In freezing conditions Peterhead started brightly and after just four minutes Neil Alexander was tested for the first time.
Ryan Strachan’s teasing free-kick delivery was met by Scott Ross but his glancing header was well saved by the Gers number one who dived low to his left.
Alexander was certainly the busier keeper in the opening stages but on 13 minutes referee Mike Tumilty had to issue the first yellow card of the game to Ryan McCann who showed a bit too much enthusiasm when he produced a late challenge on Templeton.
The official, however, waved play on when Little made a darting run into the 18-yard box but looked to be caught by centre half Ross Smith.
As expected the Blue Toon were well organised and worked exceptionally hard and Rangers looked for Templeton to provide a spark in the last third of the pitch.
But before the half hour mark it was stand-in skipper Wallace that was the architect for Rangers’ first goal.
His powerful, low shot from 20 yards was spilled by Smith and Sandaza was there to fire his shot high into the net with the keeper grounded.
It was a great moment for Fran who scored his first goal for Rangers against East Stirlingshire on August 18 at Ibrox Stadium but was out of action for almost three months because of an horrific facial injury.
On 36 minutes Peterhead looked to respond and after strong forward play from their talisman McAllister he teed up David Cox who fizzed a shot across goal but wide of target.
It was a good period of play from the home side and when Cox floated a corner kick to the back post Ross Smith’s netbound header was blocked on the line when he should have scored.
Into the second half and Peterhead immediately went in search of an equaliser with Cox dispossessing Black before firing a left foot shot over the bar.
A couple of strong challenges in midfield meant Tumilty had to step in and, after Martin Bavidge had replaced Ryan McCann on 57 minutes, McAllister and Strachan were booked for clumsy challenges on Wallace and Sandaza respectively.
The game was now turning nasty and the ref had to issue his first red card to McAllister after the striker appeared to use his hand to control the ball as he attempted to get into a goalscoring position in the 18 yard box.
With Peterhead now down to ten men Rangers looked to add more goals to the scoreline.
On 71 minutes Templeton won a 50/50 challenge before sprinting clear but his left foot shot went inches wide of the far post.
And with the clock ticking down he was then guilty of missing a great chance from 18 yards but having found acres of space he could not find the accuracy required with his shot to double his team’s advantage.
This game will not go down as one of Rangers’ best performances of the season but McCoist will no doubt be delighted with the fighting spirit his young side displayed at one of the toughest away venues in the Third Division.
The Rangers players wore black armbands today as a mark of respect for Robert Learmonth who sadly died at last weekend’s SFL fixture against Berwick Rangers at Ibrox Stadium.
RANGERS: Alexander; Hegarty, Cribari, Perry, Wallace; Hutton; Little, Black (Crawford 66), Macleod, Templeton; Sandaza (McKay 81).
SUBS: Gallacher, Faure, Shiels.
Bookings: Hutton
PETERHEAD: Smith, Cowie (Winters 79), Noble, Ross, Smith, Strachan (Sharp 74), Cox, Redman, McAllister, McLaughlin, McCann (Bavidge 57).
SUBS: Maguire, Jarvie.
BOOKED: McCann, McAllister, Strachan, Ross, Smith
SENT OFF: McAllister
REFEREE: Mike Tumilty
ATTD: 4,855