Substitute Szmodics turned the ball home from close range six minutes from time after good work on the left by Ben Dickenson, moments after Macauley Bonne had seen a goal disallowed for offside following another Dickenson cross.
Gerry McDonagh had earlier scored his first EFL goal to give the home side the lead after 20 minutes, thumping the ball in following George Maris' pass from the right.
Cambridge also had a goal disallowed when Harrison Dunk fired in following Piero Mingoia's cross 11 minutes before half-time.
Colchester's only real opportunity of the first period came in the opening moments when Dickenson could only nod Owen Garvan's cross wide at the far post.
John McGreal's side were denied 17 minutes from the end as a superb save from Will Norris kept out George Elokobi, before McDonagh fired narrowly wide at the other end ahead of Szmodics' equaliser.
Match report supplied by the Press Association.
Match ends, Cambridge United 1, Colchester United 1.
Second Half ends, Cambridge United 1, Colchester United 1.
Foul by Scott Wharton (Cambridge United).
Macauley Bonne (Colchester United) wins a free kick on the right wing.
Attempt missed. Tom Lapslie (Colchester United) right footed shot from outside the box is close, but misses the top right corner.
Leon Davies (Cambridge United) is shown the yellow card for a bad foul.
Foul by Leon Davies (Cambridge United).
Brennan Dickenson (Colchester United) wins a free kick in the defensive half.
Foul by Liam O'Neil (Cambridge United).
Drey Wright (Colchester United) wins a free kick in the attacking half.
Substitution, Cambridge United. Medy Elito replaces George Maris.
Goal!  Cambridge United 1, Colchester United 1. Sammie Szmodics (Colchester United) header from the centre of the box to the bottom right corner. Assisted by Brennan Dickenson with a cross.
Attempt missed. George Maris (Cambridge United) right footed shot from outside the box is close, but misses to the right.
Substitution, Colchester United. Macauley Bonne replaces Chris Porter.
Attempt missed. Scott Wharton (Cambridge United) header from the centre of the box is close, but misses to the left following a set piece situation.
Piero Mingoia (Cambridge United) wins a free kick in the defensive half.
Foul by Tom Lapslie (Colchester United).
Attempt missed. Gerry McDonagh (Cambridge United) left footed shot from the left side of the box is close, but misses to the right.
Corner,  Cambridge United. Conceded by Matthew Briggs.
Substitution, Colchester United. Sammie Szmodics replaces Sean Murray.
Substitution, Cambridge United. Leon Davies replaces Greg Taylor.
Attempt saved. Gerry McDonagh (Cambridge United) right footed shot from the centre of the box is saved in the bottom right corner.
Attempt saved. George Elokobi (Colchester United) left footed shot from the left side of the six yard box is saved in the bottom left corner.
Corner,  Colchester United. Conceded by Will Norris.
Foul by James Dunne (Cambridge United).
Tom Lapslie (Colchester United) wins a free kick in the defensive half.
Greg Taylor (Cambridge United) wins a free kick in the attacking half.
Foul by Rekeil Pyke (Colchester United).
Attempt saved. Luke Berry (Cambridge United) right footed shot from the left side of the six yard box is saved in the centre of the goal.
Foul by Scott Wharton (Cambridge United).
Sean Murray (Colchester United) wins a free kick on the right wing.
Substitution, Colchester United. Rekeil Pyke replaces Tarique Fosu-Henry.
Substitution, Cambridge United. James Dunne replaces Harrison Dunk.
Jake Carroll (Cambridge United) wins a free kick on the right wing.
Foul by Tarique Fosu-Henry (Colchester United).
Corner,  Cambridge United. Conceded by Drey Wright.
Attempt missed. Liam O'Neil (Cambridge United) right footed shot from outside the box is just a bit too high following a corner.
Corner,  Cambridge United. Conceded by Drey Wright.
Second Half begins Cambridge United 1, Colchester United 0.
First Half ends, Cambridge United 1, Colchester United 0.
Sammie Szmodics struck a late equaliser to earn Colchester a draw at Cambridge in League Two.