The Light Blues were trailing 1-0 at half-time after a sluggish first half performance and McDowall suggested that a tactical switch would change their fortunes.
He felt that moving David Templeton in behind Lee McCulloch and moving Andy Little wide left would have a better effect and it paid off in spades as Rangers won the game with three goals in an 11-minute burst.
McCoist said: “We came in at half-time and had a chat about things and I was very pleased with the reaction.
“I wasn’t a happy man at half-time as you might imagine. We didn’t track a runner for a one-two and lost a really poor goal and also I felt we weren’t creative enough or aggressive enough in our general play.
“The bit change was moving Templeton and to be fair to Kenny McDowall he had an idea that moving him into the hole and putting Andy Little to the left hand side would pay off and it did.
“For 25 minutes or so in the second half the game was won. We were raining in on the East Stirling goal at that time and we scored three goals and could have scored more.
“The second half performance was night and day to the first.
“I just felt in the first half we were too direct in the sense that we were playing to Lee McCulloch too directly. I felt we should have been playing into feet and down the channels.
“That changed in the second half and we benefitted from that.
“I was delighted to see Andy Little score two goals and also big Lee getting one and they have contributed so well this season. If I am critical I would like to see more from midfield and the wider areas.”
The victory over East Stirling completed a great few days for the club on the back of the SPL Commission verdict which cleared Rangers of fielding ineligible players or gaining a sporting advantage through the use of EBTS and the sponsorship announcements with Puma and Blackthorn.
McCoist added: “It’s been a wonderful 48 hours for the club. To be totally vindicated – as we always though we should be – of seeking any illegal sporting advantage and the fact we still have 54 titles is marvellous.
“The most important thing was to get back to winning ways after the draw at Stirling and I was pleased with half an hour of our play in the second half.”