The game got off to a scrappy start and it took 10 minutes for either keeper to be tested. When the chance came it was the visitors who went close when a Richard Brittain cross was left by everyone. It bounced across the six-yard line before Paul Tierney cut the ball back to Derek Adams, who hooked it wide of the mark.
Seventeen minutes Aberdeen took the lead when a pin-point cross from Jamie Smith enabled Russell Anderson to rise above the Livingston defence to power a header past visitors' keeper Roddy McKenzie.
Good play by Aberdeen's Ferne Snoyl set up Chris Clark for a shot on goal, but McKenzie was off his line quickly to block the danger at the expense of a corner. Aberdeen's Jamie Smith struck a 25-yard effort in the 33rd minute which flew over the top.
After 65 minutes the Dons doubled their lead when a Snoyl corner was flicked on at the near post by Anderson. The ball broke for Steve Lovell, who did just enough to head the ball home.
After 81 minutes the home side got a third following great play which ended with Snoyl placing the ball into the corner of the net.
Dons boss Jimmy Calderwood told RedWeb: "I'm happy with today's result and by the end of the match we were comfortable but it wasn't that way at the start of the match. We scored a good first goal but they were still causing us problems. We were slightly better in the second half, and our second goal probably killed them off.
"John Robertson will be pleased with his team's performance. They made it difficult for us and gave us a few scary moments. They just didn't get the breaks, which happens sometimes in football."