A stunning strike by Ieuan Lewis was enough for ten-man Cambridge City to edge past Weymouth at The Bob Lucas Stadium.
Cambridge's Craig Hammond was shown a red card for an off-the-ball incident with Dan Clay. The visitors' management had tried to substitute Hammond, but he was dismissed by referee Iain Parsons.
Mark Ford had several good chances to open the scoring for the Terras, but couldn't find a way past City goalkeeper Zac Barrett.
The visitors had the better of the second half, and were rewarded when Lewis turned brilliantly - before launching a perfect shot into the top corner of Simon Evans' goal.
The Terras had twenty minutes to find an equaliser, but couldn't find the net.
The loss leaves Weymouth in 16th place in the Southern Premier League, only four points ahead of 21st placed Hitchin Town.