Goals from Luke Hinsley in the first half and Jack Vann late on clinched a 2-0 success that showed what Colls are capable of as they confidently defeated third-placed opponents who have been one of the best in the division since the turn of the year.
Delighted manager Craig Rouse labelled it the "perfect away performance" as Ponte made it back to back wins and moved to within five points of tenth-placed Stocksbridge Park Steels, who have played a game more.
"We did everything we needed to do when the game was getting sticky, we put the ball in good areas and played when we had chance to play," said Rouse.
"We took our goals really well. The first is a little bit fortunate but it's going in anyway. The second probably wins our goal of the season with Vanny coming up with a rocket from 35 yards.
"Cleethorpes are a really good side, you have to give them respect and you have to come and manage things. That's what we've done. In my opinion it was a deserved three points.
"We don't want to see this season out on a whimper. We've got a lot of pride in the changing room and a lot of good players. It's important that we do ourselves justice in every performance and coming to places like this and taking three points shows that we can compete with these teams.
"In my opinion due to the start we had we are in a little bit of a false position, but we are where we are, we can't affect that now. We have to try and win our remaining games, look to next year and try to carry some momentum forward."
Colls will be aiming to make it three wins on the spin when at home to Dunston on Saturday then they face a local derby against relegation threatened Frickley Athletic on Monday (3pm).