The U’s trailed 1-0 and 2-1, but a stirring second-half display saw them triumph 4-2 to book their pace in the Johnstone’s Paint Trophy area quarter- finals.
Injuries meant the visitors had to throw an unfamiliar side together, but they gelled quickly in a lively game.
Wilder was delighted to see Harry Worley, Peter Leven and Andy Whing all gain useful pitch time, while James Constable ended an eight-month goal drought.
But for the United boss, the most encouraging sign was the way the team set about their task.
He said: “It’s been a great night for us and there were lots of positives to come out of it.
“First of all was the attitude and application of the players. I think a sign of what teams are about is how they apply themselves when games like this come about.
“I thought they were absolutely first class.
“The crowd was down, but those players showed a desire to go and get a win.
“They were behind twice but came out to win a good game.”
After strikes from Tom Craddock and Worley, Constable put United 3-2 in front 19 minutes from time with a superb angled finish on his left foot.
The striker was delighted to end a barren run which had stretched back 21 games.
He said: “It was nice to get on the scoresheet.
“I had a feeling the defender was going to hesitate, and luckily for me the goalkeeper stayed on his line and gave me the chance to get a strike on target.”
After losing six league games in a row last month, this victory against Cheltenham, wrapped up by Peter Leven from the penalty spot, made it three good results in the last eight days.
United still have a lengthy injury list, but after a win against AFC Wimbledon and a draw with Gillingham, they have regained some momentum.
Wilder added: “It’s been a difficult period and we’re not over it yet.
“We’ve got to keep on churning out results and performances, but that’s three in a row against three decent sides, so I can only take great heart from that.”