Shamir Fenelon had the first real chance of the game for the home side when he found space down the flank, but the forward drilled his strike over the bar from a tight angle.
The visitors put the pressure on the hosts as they won three corners in a row, but Josh Coulson couldn't find the net when he latched on to a cross from the right, as he guided his header past the post.
Neither side could threaten again before the end of the first half, while Michael Ihiekwe was stretchered off for Tranmere with a potentially serious injury.
Minutes later, the forward released the run of Fenelon through the middle to put him one-on-one with Chris Dunn, but Fenelon was unable to beat the keeper, who made the save to keep the scores level.
Matters got worse for the visitors when they were reduced to 10 men as Robbie Simpson was sent off for his second bookable offence.
However, Cambridge managed to rescue a point in the 89th minute as Nelson headed in an equaliser from a corner at the back post to deny Rovers the victory.