Sam Parkin's first Luton goal looked to have set Town on their way before Jamie Cureton's leveller just before half-time.
But the second half saw Hatters miss a penalty and countless other opportunities while visiting keeper Aidan Davison produced two world-class saves to tip efforts against the woodwork.
Both sides fielded unchanged sides after weekend victories; Luton against Crystal Palace and Colchester at Burnley.
In a subdued atmosphere it was the visitors who threatened first as Hatters were caught short at the back while Leon Barnett nursed an injury after attacking a fourth-minute Town corner.
Kevin Foley came across from right-back to break up the U's breakaway, but Colchester's former West Ham man Richard Garcia won the ball back and played in Cureton who could only prod at Marlon Beresford from eight yards.
Foley was involved again five minutes later as Hatters worked their first opening of the game.
The Republic of Ireland Under-21 international picked out Parkin with a deep cross into the penalty area from the right and from the striker's instant header across goal, Rowan Vine just failed to make contact at the far post.
Colchester showed some decent invention with incisive passing in Luton's final third of the field.
But Town got to grips with the visitors' slick style and created two half-openings in the space of 60 seconds in the 20th minute.
Lewis Emanuel was at the end of both as he firstly hit a 20-yard free-kick harmlessly wide after a handball by Wayne Brown.
And the bullish former Bradford man then dragged a right-foot shot wide from 14 yards after receiving a short pass from Steve Robinson and cutting inside one time Hatters target Greg Halford.
Vine was next to try his luck just before the half-hour mark as he turned inside from the left and let fly with a left-footed strike that buried itself into Davison's midriff.
Two minutes later Town did find the net as Robinson teed up Edwards to deliver a beautiful curling cross from the right and Parkin used the pace on the ball to open his Town account by glancing home a ten-yard header that went in off the far post.
Parkin should have made it two in the 39th minute as Pat Baldwin badly misjudged a back-header into the former Ipswich man's path, but he could only send his dipping left-foot volley over the bar from 12-yards.
That miss was made to look costly as Colchester's passing football paid dividends when Kevin Watson found physical forward Chris Iwelumo, whose lay-off on the edge of the area was driven home by Cureton from 20 yards.
On the stroke of half-time Garcia picked the ball up from deep, ghosted past Richard Langley and slammed a low effort past the post from 25-yards.
Town attacked from the off after the break and came close to retaking the lead when Parkin touched Vine's cross into the path of Robinson, who curled just wide from 15 yards.
Hatters should have gone ahead five minutes into the second period when Langley was fouled in the area by Kemal Izzet and stepped up to take the penalty, only to blast it against the crossbar.
Vine then had the ball in the net three minutes later, firing through Davison's legs after a surging run and pass from Edwards, but the effort was ruled out for offside.
Vine burst clear again just before the hour and after his shot was saved by Davison, he squared for Parkin to swipe at thin air with the goal at his mercy six yards out.
Davison then produced a stunning save to tip Markus Heikkinen's header onto the post in the 62nd minute, and in the melee that followed Emanuel's volley was somehow cleared by Brown.
The visiting goalkeeper repeated the trick in the 76th minute, stretching to push Foley's volley against the bar and away.
He then denied Vine twice, Foley again and Edwards as Colchester somehow hung on.