Willmott’s stunning 25-yard strike in the second half gave the Exiles all three points at Rodney Parade after visiting striker Jayden Stockley had cancelled out Padraig Amond’s opener.
Flynn said: “Robbie’s goal was a great strike. When you’re shooting from distance the most important thing is making sure you hit the target.
“He did that and he’s a very clever footballer who’s played in different positions for us. His work-rate is unbelievable and he scored one goal and made the other. He was outstanding.
“I’m delighted we got the three points against a good Exeter team.
“We conceded a sloppy goal to let them back into the game.
“I thought we were outstanding in the first half and we looked more like the team who were in the play-off final last season than Exeter did.
“At the start of the second half we were kicking it up in the air and couldn’t pass the ball but we got the win and that’s all that matters.”
Home skipper Joss Labadie had struck the post early on but Newport were ahead in the sixth minute. Willmott’s inch-perfect cross from the right was headed home by Amond.
Amond had a shot blocked before the break and Exeter’s Lloyd James was lucky to escape with just a booking following a lunge on Mickey Demetriou.
Newport defender Dan Butler cleared James’ close-range effort off the line at the start of the second half and it wasn’t long before Exeter were level.
Jake Taylor’s cross was headed home by Stockley and James then missed with a sitter of a header from six yards out. It proved costly as – out of nowhere – Newport went back ahead thanks to a stunning Willmott strike from the edge of the box.
Amond hit the side netting late on, but Newport held on through eight minutes of added time as Joe Day produced a remarkable save to deny Jake Taylor with just seconds left.
Exeter manager Paul Tisdale said: “It was a good performance and we didn’t deserve to lose. I can’t have many complaints with the way we played.
“I enjoyed watching us in action and we went body to body with Newport. Conditions were tough out there and while the pitch looked good, it was a difficult surface to play on.
“To get back to 1-1 was pleasing but means from that position we are bitterly disappointed to lose the game.”