An 84th minute strike from Alfie Potter, as well as a fantastic first-half stop from Luke McCormick, sealed an impressive away victory for the U's, just their second win in eight games.
Wilder was happy to see Potter silence a few of his critics with a fabulous finish but also believed his side fully deserved the three points after producing the more effective attacking display.
Wilder now hopes his side can take a leaf out of their book as they look to continue a push for the play-offs. "We've come up against a really good side that have been excellent all season and what they have shown and we haven't is the consistency," said Wilder.
"They are top of the league because week in week out they are at in and the challenge is now we've beaten the league leaders we certainly need to sort out our own form. And we need to show that consistency now because the players should take great belief and confidence from what they have produced.
"They worked ever so hard to open them up and we played some great football to get down the sides and Alfie has come in for a little bit of criticism but I think everybody is absolutely delighted for him after that."
Meanwhile Gillingham assistant manager John Schofield insisted that all that matters is how his side are judged at the end of the campaign. It may have been their sixth home defeat this season but Schofield maintains the Gills are focused on the bigger picture, as they still managed to retain a two-point advantage at the top.
"We have said all season we have 46 games to play and 46 games to get as many points as we can," said Schofield. "To lose any game we are not happy with but if you look over the course of the season there will be games we don't take points out of but we have to keep going.
"We have a goal we are aiming for and we will be judged by that over 46 games. Overall we had good spells in the game, good chances and [Bradley] Dack came on and was really unlucky with his first touch. If he doesn't catch it so well it probably goes in the corner but it was a great save."
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- Alfie Potter