Richard Brindley scored his first goal of the season, whipping a free kick into the top corner after Tarique Fosu was fouled.
A late penalty earned a point for the hosts, with Michael Rose sending Sam Walker the wrong way after Alex Wynter fouled Antony Evans.
There was an enforced change for John McGreal, with Tom Lapslie dropping out with a shoulder injury to be replaced by Doug Loft.
Diaz Wright came onto the bench to provide midfield cover for the U’s on the North West coast.
The U’s have started home matches very much on the front foot and McGreal wanted his side to do the same away from the Weston Homes Community Stadium.
And that was the case at the Globe Arena, with Brindley getting in on the right in the very first minute – his low cross was hurriedly cleared for a corner.
The set piece found Tarique Fosu at the far post, but his effort was blocked and cleared.
At the other end, Paul Mullin turned and shot and then an angled shot was well saved at the near post by Sam Walker.
On fifteen minutes, the hosts had the ball in the net but Kevin Ellison was deemed to be in an offside position when he shot home after Walker saved Fleming’s original effort.
Former U’s star Michael Rose was next to try his luck, but his left foot volley never looked like troubling Walker on its way wide.
That came on seventeen minutes, and two later, it should have been 1-0 to the home side.
Fleming got in down the left, pulled the ball back to Mullin but his effort was touched over the bar.
After weathering a bit of pressure, the U’s got forward on twenty one minutes and Fosu was fouled just outside the penalty area.
Wing back Brindley stepped up and confidently whipped his free kick over the wall and into the top corner to give the U’s the lead.
And it was Brindley who had the next effort, after a period of time without any goalmouth action.
There was only a minute to go when his free kick was taken by Nizic in the home goal.
Injury time at the end of the first half came and went without incident, and the U’s led 1-0 at the break.
That lead could have been doubled within five minutes of the restart, but Drey wright’s effort was deflected high over the crossbar.
Morecambe boss Jim Bentley had made a change at the break, bringing on Anthony Evans for Aaron Wildig – and the sub was causing problems for the U’s.
A long throw was cleared to him on fifty eight minutes, but his shot flew over.
Tom Eastman was first to a Murray near post corner, but could only guide his volley wide of the upright.
The U’s had another chance to extend their slender lead on sixty nine, but Fosu couldn’t keep his shot down after Nizic dropped a corner.
Chances were being created at both ends though, and Alex Kenyon hit the net four minutes later – fortunately for the U’s, it was the outside of the side netting.
McGreal made two changes in quick succession, bringing on Alex Wynter and Tommy O’Sullivan for Loft and Fosu.
The live table had the U’s in the final Play-Off position at this stage, but Rose and home sub Evans had different ideas.
With three minutes remaining, Wynter and Elokobi went for the same ball in the air, it popped out to a Morecambe attacker and the ball was swiftly moved onto Evans.
Wynter then stuck out a leg and fouled Evans just inside the box, making it an easy decision for the referee to point to the spot.
Rose stepped up and confidently dispatched the penalty into the bottom corner to give the home side a point that took them nine points clear of the bottom four with just three games remaining.
The point for the U’s wasn’t the ideal scenario but it kept them within two points of the Play-Offs ahead of Plymouth’s visit to north Essex in five days’ time.