Rachid Balabed was gifted the first real chance for the Dons in the 9th minute, when Darren Mackie's shot was saved, and Balabed came close to making it 1-0. Livingston's Alex Burns should have put the Almondvale side ahead just minutes later, but he missed from close in.
Derek Whyte picked up a booking for a rash challange on Alex Burns, and Livingston continued to cause the Don's defence problems. In the 35th minute Barry Wilson came close to giving the home side a shock lead. Aberdeen replaced McAllister and Whyte with Darren Young and Phil McGuire at half-time, and McNaughton was stretchered off in the 58th minute, and replaced with Derek Young.
David Rowson should have made it 1-0 in the 66th minute, but his header missed the target. Livingston came close a few more times before the final whistle, with Marvin Andrews coming close with a header that powered off the bar.
Aberdeen now have an even better chance of reaching the quarter-finals, with the replay being a week on tuesday at Pittodrie.