John Stewart and David Mackie wasted excellent second half chances which would have made the victory more comprehensive.
On the evidence of today's match, Livingston looked doomed to make the drop at the end of the season, for they gave away goals cheaply at one end and at the other rarely troubled the Dons' defence.
The first chance of the game came after nine minutes. Jamie Winter's corner for Aberdeen was only cleared to the edge of the area where it fell to Scott Morrison, whose right-foot shot found its way through a ruck of players but not past Burton O'Brien on the line to clear the danger.
Livingston's only chance of the first half came in the 34th minute when a long ball by David McNamee gave Ferenc Horvath the chance to chip the ball towards goal, but it went well wide of the target.
Right on the stroke of half-time the home side opened the scoring when McNaughton drove towards the edge of the area before curling a left-foot shot beyond Colin Meldrum and into the corner of the net.
In the 58th minute Aberdeen doubled their advantage when a clever ball back to McNaughton found Darren Mackie on the right, who skipped past the defence before clipping the ball to the back-post where Whelan headed home his second goal of the season and his first strike since late August.
Aberdeen should have gone further ahead after 72 minutes when a ball from substitute Chris Clark found Whelan, who drove into the area before picking out the head of Stewart, who had the simplest of tasks to head home but could only direct the ball over the top.
Livvy almost grabbed a lifeline when Derek Lilley got clear out on the right, and his cross picked out Horvath whose acrobatic effort came crashing back off the underside of the bar.