Andy Little grabbed a double, Ian Black netted his first goal for the club and Dean Shiels was also on the scoresheet as the Light Blues impressed in the second half at Ibrox.
The win allowed Rangers to move 22 points clear at the summit of the Irn-Bru Third Division and was a far cry from the 3-0 reverse at Tannadice.
"It was just what the doctor ordered," said McCoist.
"I actually thought we played quite well in the first half and I said to the boys at half-time that it was important not to feel sorry for themselves that they've not come in a goal or two up. They kept going in the second half and I was very pleased with the performance and result but the level of goal was really good as well.
"I've been saying for a few weeks now that we should be scoring more goals and the level today was very good."
Injury problems meant Little was handed his preferred role of leading the line through the middle and the Northern Irishman clearly relished the opportunity.
McCoist said: "I think Andy fancies his chances through the middle to be honest.
"Outside his goals, his performance was good as well because he led the line well. "He worked tirelessly and ran, ran, ran.
"Because he was the main focal point of our forward line, I thought he won a lot of flick-ons as well, which is an ugly side of the game but he did it well."
- Sports & Recreation