Rovers knew it was vital they successfully collected a win at Damson Park after a low key start to the Vanarama National League season.
Mellon's team delivered under pressure and their poor recent run was ended with a goal in either half.
The Tranmere manager knows the size of the three points earned and wants that to push them forward.
“It’s a very important win," he said. "We went to Solihull to get a result, there’s no doubt about that.
“We’ve played much better and got nothing this season, but considering it was red hot chilli peppers out there the lads did well.
“There will be other days when we want to play slick attractive attacking football but sometimes you have to play to the conditions, get over the line, pick up the points and get ourselves going again," the manager told the Rovers official website.
“We dealt with everything defensively, I don’t think (goalkeeper) Scott Davies has had a save to make, so every credit to the players for that and it’s a really valuable three points.”
Tranmere now face two home games - against Dover Athletic and Barrow - before a trip to Maidenhead United.