Bowman capped a remarkable personal afternoon with a stunning 'perfect hat-trick' - consisting of goals with his head, left foot and right foot - as Town saw off 10-man Cambridge at Montgomery Waters Meadow.
The striker opened the scoring with a bullet header early on as Cotterill's men held a deserved half-time lead but the hosts were made to work late on after Jack Iredale's missile hauled the newly-promoted visitors level before the hour.
But Bowman - aided by some stunning individual performances from Daniel Udoh, Shaun Whalley and Luke Leahy, who scored a late fourth - came to the fore with his second and third goal to put Shrewsbury ahead and clear.
Cambridge had midfielder Adam May sent off at 1-1 with a heavy challenge on Josh Daniels, leaving Shrewsbury to take full advantage with a clinical final 20 minutes.
The treble marks the highs and lows of football and life for Bowman, 29, who two weeks ago ended an afternoon in Ipswich Hospital after being taken off in the first half at Portman Road struggling with heart palpitations. He was later released and passed all clear to play, with the help of a heart monitor and new medication, and really announced himself as a Shrewsbury player with three fine goals, including his first at the Meadow.
"The boys are just in there now signing it for him," Cotterill said of Bowman's match ball. "It's amazing. A week is like a long time in football and the couple of weeks he's just had has been amazing.
"I'm delighted for him. I had a chat with him yesterday, and Dan Udoh, and I thought they were first class today.
"While Ryan Bowman will get all the plaudits for the hat-trick, I thought Dan Udoh was absolutely outstanding, outstanding, today Absolutely first class."
The boss added: "That's what this game does, though, doesn't it? You can have incredible lows and then highs the next.
"That's the beauty of our game, he's going to go home with a real warm feeling in his belly, with that match ball, his family will be really pleased for him.
"I'm delighted for him, because the last couple of weeks we've had with Ryan has been somewhat frightening to a degree, as I said the other week I wasn't sure if I could play him, almost, that's how serious it was at Ipswich.
"But everybody's delighted for him in there, everybody's signing the match ball so I'm sure there will be some interesting comments on that.
"The boys were just talking about it being a perfect hat-trick, left foot, right foot, header, we don't care how they go in. They could go in off his knee three times for all I care.
"But it was obviously a nice hat-trick for him and he took them very well today, that's what we need to see a little bit more of, that's the Ryan Bowman that I signed, if you know what I mean.
"I'm not saying he's going to score three goals every week because he's not, I'm not saying he's not going to have a bad game every now and then because he is, but that was really important for him.
"He's had a couple of tough weeks, so we're pleased with Ryan for that."
Udoh put in a stunning individual display despite not scoring. He stayed on the field after a heavy collision involving Cambridge keeper Dimitar Mitov, from which the Bulgarian was taken off through concussion protocols and Udoh's head was bandaged.
Cotterill said the striker has 'quite a bad dent in his forehead'.
Josh Daniels limped off after being on the receiving end of May's red-card challenge. The winger has only just returned from an ankle injury and took a heavy blow. Nathanael Ogbeta also limped off but Cotterill said none of the knocks were serious.
Town were by some way the better side at half-time despite just a one-goal lead in arguably their best half of football as an attacking threat of the season.
In all they had nine shots on target from 16 efforts at goal, evidence of a much-improved performance in the final third.
Cotterill continued: "It's the end of a tough week for us, we've had some tough games and this one was no different, some tough opposition and a little bit of travelling.
"I thought the scoreline was probably deserved for our first-half supremacy, not only the efforts on goal, but what pleased me most was nine or 10 were on target.
"We didn't have to sit here and talk about people getting blocks on us, that didn't happen.
"That (home form) is good, we want to try to get our home form good and we've managed to pick up some good results at home, we've got to try to get them away from a bit more to start to climb up the table."