Daniel Udoh’s first Sky Bet League One goal of the season lifted Shrewsbury out of the relegation zone and earned the praise of manager Steve Cotterill.
Substitute Udoh scored the winner four minutes after coming on for fellow striker Sam Cosgrove.
Luke Leahy supplied the cross for his team-mate’s header having also headed in himself in the 41st minute after Dapo Mebude’s opener for the visitors.
Udoh had not started Town’s three previous games, and Cotterill said: “Everyone knows what I think of Dan.
“But you can’t pick a team on who you like. If I did, I would pick Daniel Udoh every week.
“But he had gone off the boil a little bit. There was added pressure on him because he hadn’t scored in six league games so it was time to mix things up.
“Sam has come in and scored a couple of goals, Ryan (Bowman) has scored. It’s great to have that competition because it’s what we need.”
Cotterill also hailed Leahy’s positive contributions after he was initially involved in an unscripted three-man free-kick routine that led to the Dons breaking 80 yards to score after 33 minutes.
“Luke was my first signing when I came here,” said Cotterill. “He is a great lad with a great left foot. He can run, he can head it.”
On the set-piece howler, Cotterill grimaced and said: “They were three of our most experienced boys who got in a mix-up. When did we work on that before because I haven’t seen that one?
“But you can’t always chastise them because on another day that doesn’t end up in the back of the net.”
AFC Wimbledon have not won in Shropshire since 2012 but had the game at their mercy after Mebude’s extravagantly-celebrated goal in front of the home fans.
The Dons have now lost three successive games – two in the league – and manager Mark Robinson said: “We’ve got to bounce back. But I don’t want us to be just a pretty football team.
“Everyone says how good we are to watch but we need to be harder to play against. At times we played some decent football but didn’t have enough purpose.
“So it is very disappointing because the game was there to be won.
“But we started making poor decisions on the ball. We recognised that their biggest threat comes from wide areas but we played into their hands.
“We allowed them to get in crosses and make things uncomfortable for us. Once they got in front, they sat behind the ball and we didn’t show enough about us to open them up again.
“They are a hard-working side and get back into shape really quickly. So it was up to us to break really quickly, like we did for the goal. But we didn’t do that, we were over-indulgent.”