Celtic would have been crowned Clydesdale Bank Premier League champions if Motherwell had failed to win but that scenario never looked likely from the second minute when Higdon fired the first of two accurate long-range strikes.
Henrik Ojamaa soon added another and Higdon took his tally for the season to 24 SPL goals - and 25 in total - before Jon Daly pulled one back. Stuart McCall's side are now six points clear in second place and 11 ahead of fourth-placed St Johnstone.
Higdon has scored a variety of goals this season but arguably none as good as the opener, which had a sublime supporting role from James McFadden, who made space for himself with a drag-back that took out several opponents. The ball bobbled slightly but Higdon cut across it perfectly to send a swerving effort in off the top of the post.
Ryan Gauld shot just over after a one-two with John Rankin on the edge of the box at the other end but the opening stages were otherwise a Motherwell onslaught with McFadden running amok with some superb pieces of skill.
Chris Humphrey forced a good save from Radoslaw Cierzniak before Ojamaa netted his first goal of 2013 and only his third of the season, although the striker tops the SPL assists chart.
The eighth minute goal saw a role reversal with Higdon guiding a lay-off into the path of the onrushing Estonian, who knocked the ball past a defender before stabbing it past Cierzniak.
Darren Randolph then made some important saves, the first from Jon Daly at his near post following a cutback from Stuart Armstrong. The Irishman was then alert to deny Gauld before pulling off an impressive diving save to stop the second of two quickfire efforts from Gary Mackay-Steven.
Motherwell rediscovered their attacking intent after the interval and Ojamaa came close with an ambitious effort before Higdon made it three. The Liverpudlian took the ball in from Humphrey 20 yards out, held off and turned John Souttar before drilling the ball inside the far corner.
Willo Flood then came close with a free-kick before Daly guided the ball through the legs of Randolph in the 69th minute after Mackay-Steven had forced the ball into his path.