The U's make it five draws from seven league matches with a 0-0 stalemate at Southampton.
Both sides had chances throughout the game but keepers Davis and Cousins stayed strong and keep clean sheets.
The draw preserved the U's unbeaten record and it was their resolute defending in the second half that ensured a point was gained from the South Coast encounter.
John White came in at right back in place of Brian Wilson, who picked up an early ankle injury in that draw with Plymouth Argyle.
New loanee Liam Henderson started the game on the substitute's bench, as the U's looked to improve on their eighth place in the League One table.
The U's other Henderson, Ian, joined him on the bench, having recovered from his knee injury.
The Saints also made just one change from the side that lost at MK Dons on Wednesday, with former Southend striker Lee Barnard coming in for David Connolly.
Also included in their line-up was Dean Hammond, who joined the Saints from the U's at the beginning of last season.
If the home fans were expecting their side to take the game to the U's, they were mistaken, with the visitors being on the front foot early on.
In only the third minute, a good ball from David Perkins found David Mooney but he was denied a shot when a defender slid in to clear.
Mooney did get a shot away a minute later though, his right foot effort zipping just wide of the post, with Davis rooted to the spot.
The home side did have a shot on target on six minutes but it was comfortably saved by Mark Cousins and the U's were back on the attack seconds later.
This time, Perkins was involved down the right with Ashley Vincent and from John White's cross, Anthony Wordsworth could only find Davis' hands with his header.
Saints had certainly been on the back foot early on but they started to gain a foothold in the game and went close on thirteen minutes, Lambert's free kick clipping the side netting.
Cousins had to dive sharply to his right to save from Schneiderlin on twenty minutes, as the game became more even.
An injury to Marc Tierney saw him replaced by Lloyd James on thirty three minutes and a minute later, David Mooney went into the book, receiving a yellow card for persistent foul play.
The home side were getting desperate for a goal before half time and tried their luck twice from distance in the final five minutes of the half.
First, Lee Barnard's speculative shot from over thirty yards out flew high and wide and then Lambert's weak effort was deflected for a corner, which came to nothing.A few minutes later, Lambert looked like he was clear but a last ditch tackle from Lloyd James, returning to his former club, prevented a shot coming in.
With time ticking away in the first half, Andy Bond, who had scored four already this season, volleyed goalwards but Davis was in the right place to take it comfortably.
The half time whistle went a couple of minutes later and the teams being level was probably about right for the first forty five minutes.
As the teams ran out after the break, Pat Baldwin looked like he was limping and after a couple of sprints before the referee came out the tunnel, he decided that he couldn't start the second period.
Paul Reid came on and he was involved in a real rearguard action for the U's for the majority of the second forty five minutes.
Lambert only took three minutes to have his first effort, shooting over the bar after finding space just outside the U's penalty area.
Ten minutes later, a shot was deflected for a Saints' corner and from the resultant set piece, Lambert's volley was superbly saved by Cousins diving smartly down to his left.
On the hour, right back Butterfield shot wide when well placed, and he should really have done better, before Barnard headed wide.
New boss Nigel Adkins made a change and one of his subs, Lee Holmes almost scored with his first touch, shooting narrowly wide of the post.
With eleven minutes remaining, two corners in quick succession caused problems in the U's area, then Lambert's free kick was hit straight into the wall.
With the U's under the cosh, an unlikely winner nearly materialised, with Vincent having his shot saved by Davis.
A Magnus Okuonghae clearance was flicked on by Vincent and it looked like Kayode Odejayi, who had replaced Mooney, was in on goal.
Great pace by Fonte made Odejayi turn out but he found Vincent, who only had Davis to beat - unfortunately, the Saints' keeper was equal to Vincent's low effort.
As the game went into injury time, it was a case of Lambert versus Cousins, with the U's stopper coming out on top, saving twice from free kicks.
The second in particular was special, as he dived full length tp his left to fingertip the ball to safety, with the final whistle going before the home side could take the corner.
It was backs to the wall stuff for the U's in the second half but resolute defending ensured a clean sheet, a fifth draw in seven league games and a preserved unbeaten record.