They dominated most of a low-key game against Boston, before being caught out at a set-piece in the 83rd minute from which the visitors scored the winner. Andy Kirk's goal was from their first shot on target of the afternoon.
The Northern Ireland international was the big difference between two toiling teams, snapping up his chance when the ball bounced through to him in a crowded box following a free-kick to get his 13th goal in 16 starts.
His opposite number Jermaine Easter had three times as many opportunities but failed to hit the target once.
Midfielder Justin Walker went closest to giving Cambridge the lead their overall play deserved when he hammered in a shot from the edge of the box in the 75th minute, but Pilgrims keeper Nathan Abbey pulled off a brilliant save, flicking the ball over the crossbar.
It looked rough justice for Cambridge on the hour when winger Shane Tudor appeared to be pulled back in the penalty area by Boston skipper Paul Ellender, only for referee Robinson to award a free-kick against the forward.
The first half looked like a real hangover from the New Year's Eve celebrations, with neither side creating any goalmouth action.
The only time a goalkeeper was required to make a save was in the 26th minute when Abbey was not really troubled by a header from Andrew Duncan at a corner kick.
Steve Thompson's first game in charge might have had an even more unjust scoreline when, two minutes after his goal Kirk beat the keeper with a header, only for Stuart Bimson to head it off the goal-line.
Thompson at least managed to send out a more organized-looking side, pleasing the fans by restoring three players, Tudor, defender Adam Tann and winger Abdou Elkholti to the starting line-up.
Boston looked suitably tentative for a team who had won only one of their 12 away matches this season, but in Kirk they had the only player who looked anything like dangerous inside the box.