The boss rolled the dice with 10 minutes to go at Adams Park when he switched his formation from a 3-4-1-2 to a 4-3-3.
And the changes paid dividends when second-half substitute Tom Bayliss was fouled in the box, and referee Lee Swabey pointed to the spot.
Luke Leahy was calm under pressure, and his powerful effort went straight down the middle past the diving Dickinson. The players celebrated in front of 282 joyful Shrewsbury Town fans.
And Cotterill praised the fitness of his players after the game was played in temperatures of up to 34 degrees. The match was stopped midway through each half for the players to re-hydrate.
He said: "I thought that our fitness levels were good as the game went on.
"Which I think that was really really important for how we finished the game.
"Especially on a day like today.
"I thought in the second half they were excellent.
Town went behind through a Garath McCleary strike early in the second half after he picked up the ball in midfield.
And the Town boss was disappointed with the goal they conceded saying they did not learn their lesson from the first half.
"We could have been 1-0 down from exactly the same scenario in the first half.
"So we didn't learn our lesson on that, and even though we had spoken about that at halftime, that really caught us cold.
"The only thing it did do is it spurred us into action because then all of sudden we looked like we were angry and we were going to join in."
In the 60th minute, Town equalised. George Nurse launched a throw into the Wycombe penalty box. The ball was flicked on by Tom Flanagan making its way to Pennington at the back post, who headed home.
And with one-minute remaining Shrewsbury snatched all three points from the penalty spot.
The Town boss was pleased they won the game after the changes he made with 10 minutes left on the clock.
He said: "Our substitutions showed that we went for the game.
"We flipped, we went to 4-3-3, and I think that gave us a lot more impetus.
"I think they went for it most of the game, if I am brutally honest.
"I thought they played a good game.
"But we have been on the back end of those when we have played well enough in a game and not got the points."