The home side were unbeaten in six games before this fixture but the Robins ended the game well beaten as Cambridge, led by an impressive performance from the front two of Dave Kitson and John Turner, scored once in the first half and twice in the second.
Cheltenham began the game well enough but things started to go wrong for them in the 25th minute when key centre-back Michael Duff limped off with an injury.
Five minutes later Cambridge took the lead when Luke Guttridge produced a superb crossfield pass for Turner and his cross was met with a diving header from Kitson.
Robins manager Bobby Gould made an immediate change, sending on Martin Devaney for Mark Yates and the move bore some fruit as the home side enjoyed a good spell either side of half-time.
Cambridge goalkeeper Shaun Marshall made superb saves from Devaney and Lee Howells and defender Stuart Bimson was forced to clear a header from Jamie Victory off the line.
But Cambridge stuck to their task and added a second goal on the hour when Turner sent Kitson clear with a throughball, the flame-haired striker beating goalkeeper Shane Higgs with a low drive.
With the visitors sitting deep and defending with calm efficiency there was no way back into the game for the home side.
Substitute Lloyd Opara completed a joyful afternoon for the U's three minutes from time when he latched onto a pass from Guttridge and rolled a shot beyond Higgs.
"It was a complete performance from everyone out there." enthused Cambridge manager John Taylor.
"Dave Kitson will rightly get all the plaudits but it was an excellent team performance and young John Turner alongside him was superb. When he fills out he could be as good as anything this club has produced." Cheltenham's veteran striker Bob Taylor said: "We came out saying the right things and wanting to do the right things but just didn't put it into practice.
"The players have to look at themselves because we didn't do the things we were asked. I hope it's only an off day because I know we are better than that."