Sandaza blasted home the rebound after Peterhead goalkeeper Graeme Smith had spilled David Templeton's shot after the half hour.
Any hopes the home side might have had of a comeback were then dashed as Rory McAllister was sent off for a second bookable offence midway through the second half.
"I'm delighted for him," McCoist said on Sandaza. "He got his reward for all his endeavours last week as well.
"He played really well last week without scoring and you feel the crowd willing him to get a goal. I think there was an extra cheer when he did score.
"I thought it was a great goal. It was well-worked by Templeton and Lee Wallace, and I thought he gambled well and finished it well.
"He's taken a whack as well, he got a boot in the face - I think he's just one of those guys! I'm hopeful that the goal will give him the confidence and opens the door for him to score a few more goals."
McCoist did feel, though, his side need to be more clinical in front of goal to finish their opposition off.
"Our decision-making in the last 20 minutes was poor," he said. "And our finishing isn't at the level it should be.
"We're creating chances and should make it more comfortable in the last 10 or 15 minutes.
"When you don't take your chances, you run the risk of losing a free-kick or a set play. Thankfully, that didn't happen."
Peterhead were clearly keen to take the game to Rangers and had particularly strong spells both early and late in the game.
Recent signing David Cox was left disappointed to have lost, but feels his side have shown there is not much between them and the 'Gers, who are now 19 points clear of second-placed Queen's Park.
He said: "We started really well in the first 10 or 15 minutes, but we started to drift out the game a bit.
"We're all a bit disappointed we didn't take something from the game. It didn't help with Rory getting sent off, but all in all I thought we did pretty well.
"I wasn't here at the start of the season but we did really well against them, and then at Ibrox we should have scored in the first five minutes and it'd have been a completely different game.
"We've done well every time we've played them, so we need to kick on and see where it takes us in the rest of the season."
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