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.
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. Robert McHugh responded moments later with a side-footed effort which was deflected for a corner, following Chris 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. The game had barely restarted when Humphrey powered up the right wing and crossed for Higdon, who arrived in the box at pace to slam home from close range.
Inverness enjoyed several raids forward, Andrew Shinnie creating a good opportunity for David Raven, whose shot was blocked by the goalkeeper. The Highlanders reduced the deficit on 27 minutes when Foran netted a looping header from Owain Tudur-Jones' cross, the ball curling beyond Randolph at the far post.
Motherwell took the initiative after the break and saw Keith 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.
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. Motherwell made it 3-1 on 71 minutes when Higdon intercepted a poor backpass and finished off the base of the left-hand post. Higdon completed his hat-trick in style by lashing high into the net from Henrik Ojamaa's cross.
Inverness' woes were complete two minutes later when they were awarded a penalty for Jonathan 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.
Meanwhile, Dundee won their first Clydesdale Bank Premier League match of the season after a 1-0 victory over Hearts at Tynecastle.
Ryan Conroy's third minute penalty was all that was required for Dundee to secure all three points and lift them off the bottom of the table.
Hearts dominated the attacking possession but couldn't beat an inspired Rab Douglas in the Dundee goal. The veteran goalkeeper made a string of impressive stops including John Sutton's first half spot kick.
The hosts made one enforced change to the team that drew 1-1 with Liverpool in the Europa League play-off on Thursday. Anfield scorer David Templeton completed a switch to Rangers on transfer deadline day and was replaced in the starting line-up by Dale Carrick, the youngster making the first start of his professional career. New signing Ryan Stevenson had to be content with a place on the bench.
Visitors Dundee made two changes to the side that exited the League Cup at the hands of Queen's Park, as striker Colin Nish was recalled to the starting line-up in place of Steven Milne while Graham Webster dropped out to make way for the fit-again Lewis Toshney.
Nish made an immediate impact by helping to give Dundee the lead inside three minutes. The former Hibs striker turned into the penalty area and was needlessly tripped by Hearts captain Marius Zaliukas. Referee Craig Thomson showed no hesitation in pointing to the penalty spot, and up stepped Conroy to smash the ball low past Jamie McDonald.
Hearts pressed their opponents looking for a quick route back into the match, but they had to wait 20 minutes for their first sight of goal. Even then it was a speculative effort as Callum Paterson's 30-yard attempt was cautiously pushed over the bar by Douglas.
The home side were then rewarded a route back into the match as Ryan McGowan wriggled his way through the penalty area before being tugged down by Toshney. Again, Craig Thomson immediately awarded a penalty and although Sutton's spot-kick was hit with power and accuracy, it was brilliantly parried away by Douglas diving low to his right hand corner.
Paterson showed pace and power to leave two Dundee defenders in his wake, but scuffed his shot from the edge of the box on his weaker left foot.
With the first half drawing to a close, fellow teenager Carrick then went close to restoring parity. The attacker's swivelled shot from 18 yards had to be tipped round the post by a stretching Douglas.
For the second half, Hearts boss John McGlynn introduced Stevenson for his second Hearts debut in the hope of injecting life into his side's struggling attack. Withdrawing was Sutton in a like-for-like swap in terms of position and experience, but it was the youngsters who again went closest to levelling the match. Novikovas' cutback found Paterson in the penalty area but he fired wide from 10 yards.
It wasn't long, however, before Stevenson began to influence proceedings. On the hour he produced a save from Douglas and then from the resulting corner he beat the keeper with a glancing header, only to see Conroy clear the ball off the line.
For the final 25 minutes Hearts were relentless in their pursuit of a goal but couldn't find their way past a Dundee side that defended strongly in the face of a continuous wave of attacks.
For all Hearts pressure there were few chances and the game finished with nothing to show for their efforts.
- Chris Humphrey