Tom Hateley had opened the scoring for the hosts directly from a 10th-minute corner and Higdon netted the first of his three goals a minute later.
Richie Foran reduced the deficit to 2-1 before half-time but Higdon added another two goals in eight minutes of the final quarter of the game, with Inverness seeing a late penalty saved.
Motherwell made five changes to the team which lost at Levante in the Europa League on Thursday.
Starting berths were handed to Nicky Law, Hateley, Chris Humphrey, Robert McHugh and Zaine Francis-Angol, the latter three having appeared as substitutes in Spain.
They replaced Jamie Murphy, Henrik Ojamaa, Stuart Carswell and Steve Hetherington, all of whom were on the bench, and Stevie Hammell, who dropped out of the squad.
Visiting captain Foran returned from suspension with Billy McKay dropping to the bench following Inverness' midweek victory at Arbroath while in a late pre-match change David Raven started in place of defender Simon King.
Inverness' Ross Draper had the first effort of the game, trying a shot inside two minutes which goalkeeper Darren Randolph had to dive to turn round a post.
McHugh responded moments later with a sidefooted effort which was deflected for a corner, following Humphrey's good work down the right.
Motherwell then seized control with two rapid-fire goals, beginning as Hateley put his side ahead on 10 minutes, his corner curling in at the near post with Inverness goalkeeper Ryan Esson unable to stop it.
The game had barely restarted when Humphrey powered up the right wing, evading attempted tackles from both Graeme Shinnie and Draper, before reaching the byline and crossing for Higdon, who arrived in the box at pace to slam home from close range.
Aaron Doran and Owain Tudur-Jones both tried their luck with half-chances which failed to trouble Randolph, while Hateley fired in a shot from the left which Esson had to tip over the bar.
Inverness enjoyed several raids forward, Andrew Shinnie creating a good opportunity for Raven, whose shot was blocked by the goalkeeper.
The Highlanders reduced the deficit on 27 minutes when Foran netted a looping header from Tudur-Jones' cross, the ball curling beyond Randolph at the far post.
Home captain Keith Lasley blazed over on the half-hour and Higdon tried a chip from the edge of the area which drifted over the crossbar, while Foran had a good chance to equalise two minutes before the break when he latched onto a long ball, his initial shot saved by Randolph before he headed wide with the rebound.
Motherwell took the initiative after the break and saw Lasley come agonisingly close with a diagonal effort seven minutes after the restart.
McHugh then threw himself at a Law cross but was unable to connect just feet from the goalline, with Higdon hitting the side netting on 57 minutes.
Inverness had already seen Foran rise to meet Doran's free-kick from the right flank, but the header was easily claimed by Randolph.
The hosts believed they had a penalty claim on the hour when Fraser Kerr was challenged inside the box, but had to settle for a corner, with Jonathan Page heading off target from Law's delivery.
Motherwell made it 3-1 on 71 minutes when Higdon intercepted a poor backpass and burst into the box, doubling his tally for the game with a finish which went in off the base of the left-hand post.
Higdon then completed his hat-trick in style by lashing high into the net from Ojamaa's cross after the substitute made an impressive run down the right wing.
Inverness' woes were complete two minutes later when they were awarded a penalty for Page's foul on Foran, only for Shinnie's effort to be expertly saved by Randolph, who dived to his right to push the ball to safety.
