A goal from Ian Thomas-Moore earned Rovers a 1-1 draw and a point at the Weston Homes Community Stadium.
A fine injury time save from Colchester keeper Ben Williams denied Les Parry's side all three points but the draw kept them within two points of both Exeter City and Gillingham.
The captain netted his side's goal inside the first ten minutes after Anthony Wordsworth had earlier struck for the U's.
There was one change to the side that started at Brentford, with Shaleum Logan returning from a hernia to take the place of Gareth Edds. The change meant Marlon Broomes reverted to centre back with Ash Taylor moving into the centre of midfield alongside John Welsh and Joss Labadie. Chris McCready recovered from injury to take a place on the subsitutes' bench.
Rovers didn't make the most of an early corner and on four minutes they were punished. After Tranmere failed to clear the ball from the area, Colchester's Anthony Wordsworth volleyed in, with his low shot giving Peter Gulacsi little chance and the home side the lead.
But the advantage lasted barely two minutes. An attack that started through John Welsh saw Joss Labadie's well hit effort saved by Ben Williams but Ian Thomas-Moore was on hand to turn in the rebound to the delight of the travelling support.
Thomas-Moore volleyed wide from a Savage cross on nine minutes and the pair almost combined again four minutes later but the ball wouldn't drop kindly and Colchester cleared the danger.
Another long distance shot from Thomas-Moore missed the target on 18 minutes while Wordsworth headed wide at the other end.
A long break in play saw Ashley Vincent carried off from the pitch on a stretcher and replaced by Ian Henderson on 33 minutes.
Zoumana Bakayogo fired over the bar from outside the area on 37 minutes while Wordsworth went close to a second six minutes later but his header went wide of goal.
The home side had a free kick in a promising position deep in first half injury time but Gulacsi did well to catch David Prutton's curler and the half ended all square.
An early second half 25 yard shot from Savage failed to test Ben Williams in the Colchester goal and Wordsworth missed from a similar distance at the other end soon after.
A low shot from Welsh missed Williams' goal on 58 minutes and Ian Henderson brought a save out of Gulacsi as the action swung from one half to the other, with both sides looking for the crucial second goal.
Andy Robinson replaced Craig Curran with more than 20 minutes remaining but the striker had not had a touch when Gulacsi did well to deny Kevin Lisbie.
A shot from Thomas-Moore hit a defender on 72 minutes and Robinson fired over the bar soon after from the edge of the area.
Labadie missed from 25 yards on 75 minutes while the home side were given a chance from Taylor's stray pass with three minutes remaining but substitute Kayode Odejayi put his low effort just past the far post.
Four minutes of added time gave both sides the chance of clinching a late winner and some neat play from Robinson earned a corner before Prutton was shown a red card for his second booking of the game.
In the final moments of the game Marlon Broomes unleashed a fine 20 yard volley but Williams produced a wonderful save to push the ball behind for a corner.
Colchester: Williams, Reid, Tierney, White, Okuonghae, Wordsworth, Prutton, Izzet (Hackney 60), Gillespie (Odejayi 75), Lisbie, Vincent (Henderson 33). Substitutes not used: Cousins, Heath, Platt, Fox.
Tranmere: Gulacsi, Logan, Broomes, Goodison, Bakayogo, Welsh, Taylor, Labadie, Curran (Robinson 67), Thomas-Moore, Savage. Substitutes not used: Coughlin, McCready, Barnett, Edds, Gornell, Bain.
Referee: Phil Crossley
Yellow cards: Curran (26), Prutton (41), Lisbie (45), Labadie (45), Gillespie (53)
Red card: Prutton (90+2)