Two first half goals ensured that this game ended all square, as the visitors passed up a number of chances to have helped themselves to all three points.
First Josh Ginnelly was in plenty space to fire hone from a right wing cross, then Simon Heslop equalised with a delightful header from a Kayden Jackson cross.
Early scare as out of nothing Simon Richman fired in a shot that crashed against the Wrexham crossbar.
The home side took the lead on 12 minutes when they broke up a Wrexham attack and Ryan Crowther raced down the right wing before delivering long cross that allowed Ginnelly to fire home from 12 yards with the Wrexham defence stretched.
On 18 minutes, Sean Newton did well to win the ball out wide and his deep cross was aimed at Jackson, but full back Adam Griffin was able to head away while facing his own net.
There were bookings for either side as Fyfield and then Crowther had their names taken, by Oxfordshire referee John Busby.
The home side had another chance when Taylor had to come off his line and Ginnelly's chip carried over the Wrexham crossbar.
The Welshmen were level on 30 minutes, when Simon Heslop scored with a lovely flick header, diverting the ball away from the keeper, after Jackson’s cross in from the left.
Moments later, both Heslop and then Jennings fired in shots that were blocked by the home defence in quick succession.
There were seven minutes of the first half left, when Scott Leather fired a low shot goalwards from 25 yards, but Taylor was down to it and made a good save.
Our first real effort in the second half came on the hour mark, when Moke played a ball in for Jackson, his shot was on target but a defender's boot took sting out of it.
Leather headed off the line from Jennings chip, following a series players slashing at the ball but not making proper contact in the six-yard box.
Then another defender cleared off his own goal line from Evans, with Hudson’s header at the ensuing corner flashing wide.
Rankine responded with a close range header that somehow ended up in the arms of Taylor!
On 75 minutes, more Wrexham pressure saw Newton head the ball back into the home box where Beck was clear, but he couldn't make clean contact with the goal at his mercy.
Two minutes later, Jackson and Beck were causing more problems for the home defence, but only winning a corner. Then Alty broke quickly up field, with Crowther firing wide when in a good position.
Fyfield great 50 yard run to the line, pulled back for Jackson, but his touch was off target from six yards.
With only minutes left, Jennings was next to try his luck, but it carried high over the travelling Wrexham supporters on the open terrace.
Altrincham: Deasy, Sinnott, Griffin, Leather, Holness, Crowther (Mottley-Henry 85), Ginnelly, Moult, Richman, Rankine, Margetts.
Subs: Heathcote, Reeves, O'Keefe, Lawrie.
Wrexham: Taylor, Carrington, Smith, Hudson, Fyfield, Newton, Heslop, Moke (Beck 62), Evans, Jennings, Jackson.
Subs: White, Fowler, York, Gray.
Referee: John Bushy (Oxfordshire)
Away: 335 away terrace, plus those in the main stand
Altrincham: Crowther (21, foul), Richman (42, foul)
Wrexham: Fyfield (15, foul)