In-form Cambridge striker Scott Rendell booked the Us' place in the third round of the FA Cup as his 26th-minute penalty was enough to beat Weymouth 1-0.
The former Crawley striker netted his 15th goal of the season from the spot after he had been felled by Justyn Roberts and that proved enough for Jimmy Quinn's men.
The U's came flying out of the traps and in the third minute Gavin Hoyte's 25-yard drive was brilliantly tipped over by Jason Matthews.
But the goal came when Rendell was hauled down in the box by Roberts before picking himself up to send Matthews the wrong way from the spot.
However, the hosts only had the lead at the half-time thanks to Stephen Reed's brilliant clearance from a Vernazza cross with three Weymouth players poised to strike at goal.
The first chance of the second half came in the 68th minute when Scott Doe made a superb clearance to deny Lee Boylan, before Stuart Beavon sent Sido Jombarti clear at the other end but Peters cleared the danger with the Portuguese midfielder poised to fire in an equaliser.
Two minutes from time Anton Robinson corner flicked off Potter and onto the crossbar but Cambridge held on.