Cheltenham manager Mark Yates toasted goalkeeper Scott Brown and the Whaddon Road crowd after the 1-0 win ended Gillingham's impressive nine-match unbeaten run.
Defender Michael Hector scored the only goal, heading home a Billy Jones corner midway through the second half. It denied already-promoted Gillingham a League Two title party upon boss Martin Allen's return to his former employers, and left the fourth-placed Robins just two points off the automatic promotion places themselves.
Yates said: "Scott trained on Thursday and had a massive whack on the foot. To be fair to him and physio Ian Weston, they have got a proper egg-sized lump down and that shows the character he has and the character we have in the squad.
"He deserves a special mention because he has put a shift in for the boys. Connor Roberts was all set to play but Scott has played through the pain - he had a couple of painkillers and put in a lot of hard work between Thursday and now.
"The crowd were good and were our 12th man - and we need a good following down at Exeter (next Saturday). The players have shown when we have got the support and the backing that we are a good side. We have beaten some good sides here and it's often when there is a decent crowd and we rise to the challenge."
Aside from Hector's header, Cheltenham had other chances as they pinned the league leaders in their own half for much of the second half.
"We were outstanding and have taken four points off the probable winners of the league - and the best team in the league," Yates said. "We showed we had that aggression and that competitive edge."
Despite defeat, Gillingham remain six points clear of Port Vale with just two games remaining and boss Allen is now looking to seal the title at home to AFC Wimbledon next weekend.
"Our players battled and we had a few half opportunities," he said. "We did alright and the players performed well but Cheltenham did very well. One little error has cost us the game and we will have to live with that. We came here to win and I'm disappointed that we didn't.
"But the players have given everything. It would have been nice to get a goal at the end to go up as champions but we can look forward to next Saturday when a win will make us champions."