Centre-forward Main reacted sharply to glance a flicked headed from a spinning deflected cross over Burton's goalkeeper for a sixth-minute opener.
Harry Chapman slammed in a volley before the hour to double Salop's lead and Town held on comfortably despite Sean Clare halving the arrears for the hosts.
Main's second goal, and first from open play, since arriving in January caused some confusion with suggestions Nathanael Ogbeta's diverted cross may have spun and bounced straight over Ben Garratt.
But Main was in no doubt and said bullishly: "I don't know what the confusion is, maybe it looks different on camera, but it's certainly my goal.
"There is no doubt! It was my goal and you won't be taking it away from me.
"I had to time it well, it took a deflection and I had to judge it and get in there and slightly glance it over the keeper.
"I think the keeper was stuck and the little look back was just to make sure it had gone in, I don't know if they were trying to claim not but it was clearly over the line.
"It was pleasing to get ahead early doors on the road."
The win means Salop are unbeaten in four games, having taken eight points from a possible 12. They remain 17th in League One but with 50 points and a number of sides above them in sight.
Shrews sealed a fine away win without the likes of Matija Sarkic, Ollie Norburn and Aaron Pierre.
Main agreed with Town first-team coach David Longwell's assessment of a big night's work for Shrewsbury in Staffordshire, where Burton have been in excellent form under Jimmy Floyd Hasselbaink.
The former Middlesbrough and Aberdeen frontman added: "We had to work for it no doubt, three points on the road are always tough but in that fashion it was backs-to-the-wall for large parts with their set-plays.
"It wasn't pretty, not nice to watch, but in terms of the table and where teams are I think it is a pretty big three points and we can be looking up rather than behind us."
Longwell said: "It's a fantastic win for us, a really big three points. Burton have been on a really good run and it was a big result for us to come here and get the victory.
"Of course he (Main) is claiming it! He definitely got a touch - and even if he didn't he'll claim it! It's well-deserved, he was outstanding.
"People don't realise how tough it is on players playing Saturday-Tuesday, it's so demanding physically. Their attitude to work and compete is second-to-none.
"Chappy has got real quality, he's added to his game with such a shift out of possession, he got his rewards tonight, the manager talks about that a lot, his quality of goals is unbelievable."