The Steelmen completely outplayed their hosts during a first half in which Higdon and Jamie Murphy, via a deflection, both netted.
Chris Humphrey added a third before the Pars finally made a game of it in the final quarter after substitute David Graham's shot deflected in off team-mate Joe Cardle.
Cardle gave the hosts the unlikely prospect of salvaging a point as he netted a deflected goal on the break in the final stages but Higdon grabbed his second within a minute.
Tim Clancy made an assured debut at centre-back on Saturday after completing his move from Kilmarnock and replacing Shaun Hutchinson, who had a hamstring injury.
Motherwell again bounced back from last weekend's 3-0 defeat by Rangers, which was followed by a 4-0 cup win at Clyde, and they deserved their win thanks to a confident display of passing in midfield with Nicky Law at the hub of their moves.
Dunfermline had restored Gary Mason, Cardle, Martin Hardie and Andy Kirk to their starting line-up following their Scottish Communities League Cup defeat by East Fife, but they were up against it from the start as Motherwell kept possession for long spells in their half.
They were rewarded in the 11th minute when Higdon finished off a probing move. A short free-kick 35 yards out was rolled to Steve Jennings, who found Higdon and the former St Mirren striker played a tight one-two with Keith Lasley before curling the ball into the bottom corner from 18 yards.
Higdon, who opened his Motherwell account at Broadwood in midweek, was soon close to reaching Humphrey's excellent cross but Paul Gallacher grabbed the ball off his head.
Motherwell continued to dominate and Tom Hateley hit the post with a 30-yard free-kick, the ball then bouncing off Gallacher's hand and away. Murphy claimed he was pushed in the box by Jason Thomson as he chased the rebound but referee Euan Norris waved away the appeal.
Murphy was soon celebrating, though, as Motherwell went two ahead in the 25th minute. The forward broke away from Mason and his 20-yard drive deflected off Alex Keddie and beat Gallacher inside his near post.
Visiting goalkeeper Darren Randolph was a virtual spectator throughout the first half as Dunfermline struggled to get hold of the ball or move up the park.
Keddie prevented the game going completely beyond the Pars before half-time when he blocked Higdon's volley from close range after Law and Stevie Hammell overloaded down the left.
Dunfermline made an initial attempt to push more men forward after the break but Motherwell quickly picked them off on the break.
Murphy threatened with a run and cross and Keddie cleared off the line from Law after Jennings had played him clear round the outside.
But there were enough Dunfermline players back when Humphrey netted the third in the 55th minute.
There appeared little danger as the winger attacked the home defence from the right wing but they sat off and he cut in to fire a powerful left-foot shot in off the far post from 14 yards.
Home manager Jim McIntyre brought on all his substitutes before the 61st minute with David Graham, Ryan Thomson and Paul Willis charged with changing the course of the game.
But it was a slice of luck that got them back in it in the 69th minute. Graham let fly from 30 yards and the ball hit off Cardle's back and beat Randolph.
Randolph made his first save of the game when he held Andy Kirk's header following a cross from Jason Thomson, who soon blazed over from 20 yards after another decent attack from the hosts.
Motherwell looked to have killed the game off but they were caught on the break in the 88th minute after Lasley lost the ball inside the Pars half.
The visiting defence was exposed and Cardle ran to the edge of the box before unleashing a low drive that took a major deflection off Stephen Craigan and beat Randolph.
However, Motherwell quickly extended their lead to a more accurate portrayal of the game as Higdon netted his third in two games in the last minute.
Motherwell played the ball from the back and Humphrey found Law inside the box with the English midfielder sending in a low cross that Higdon stabbed home from close range.