After netting against Hamilton last weekend and at Inverness in midweek, the striker made it three in three matches as the Bairns broke their run of three straight draws.
In a game lacking clear-cut chances, an excellent winning goal lit up the Falkirk Stadium as Higdon finished off a flowing four-man move to drive home from the edge of the penalty area on 37 minutes.
Motherwell, perhaps jaded from their endeavours in holding Rangers in midweek, were not at their best but were left to reflect on a glorious chance passed up by Marc Fitzpatrick with the game goalless.
Falkirk manager John Hughes made just one change from the side that drew 1-1 at Inverness in midweek, hamstring victim Neil McCann dropping out for Graham Barrett.
Under-pressure goalkeeper Scott Flinders retained his place despite his late error for Adam Rooney's equalising goal in the Highlands.
Motherwell also made one alteration from the team that drew 0-0 on Wednesday, with Chris Porter dropping to the bench and Scotland striker David Clarkson starting.
Given the windy conditions, Falkirk typically started playing their passing game in a bid to combat the weather.
However, it was the aerial route that almost paid dividends through the hosts' first chance on seven minutes.
A short free-kick was played back to Dean Holden and his lofted cross was met by Higdon but his header was straight at Graeme Smith.
Falkirk, though, breathed a massive sigh of relief in the 12th minute after uncertainty at the back nearly led to a Motherwell breakthrough.
John Sutton's back header caused chaos in the Bairns' penalty area with neither defence or an edgy Flinders taking charge.
Under pressure, Clarkson slid the ball just wide of the right upright.
Higdon then replied with a skewed shot wide from 15 yards after Steve Lovell had laid the ball off to him.
Sutton also tried his luck from distance but Flinders watched the ball trundle past the post.
Clarkson went closer on 20 minutes, his low angled drive held by on-loan Flinders at the second attempt as Stephen Hughes lurked.
Falkirk's final ball was letting them down, with the visitors looking more menacing in attack.
In the 26th minute, McGhee's side really should have been ahead.
A Hughes cross from the left found Fitzpatrick in space but Lee Bullen brilliantly blocked his close-range effort.
However, the rebound fell back to the midfielder and with the goal gaping he somehow placed his seven-yard shot wide of the right post.
Falkirk forced a series of corners but none came to fruition as a drab game cried out for a goal.
Suddenly, on 37 minutes, the breakthrough arrived as Falkirk grabbed a superb, well-worked opener.
Lovell's lay-off at the halfway line found Scott Arfield who swiftly moved the ball out to Barrett on the right.
The Irishman's quick, accurate cross picked out Higdon, who chested down before rifling an 18-yard drive into the far left-hand corner for his seventh of the season.
It was a cagey opening to the second half, before Sutton shrugged off the attentions of four players to curl in a left-footed effort that Flinders smothered away.
At the other end, Holden's cross allowed Barrett to make a diving header that was comfortable for Smith.
McGhee made an attacking change on 57 minutes, withdrawing Keith Lasley for Porter to the displeasure of the away support.
However, on the hour mark, Falkirk twice went within inches of doubling their lead.
Lovell neatly played in the on-rushing Barrett who was brilliantly denied by Smith's left boot.
The rebound fell kindly back to the ex-Arsenal youth player who saw his next attempt catch the outside of the right post.
Burton O'Brien then slipped in Lovell on the left but as Smith came racing out from his goal, the striker's long-range chip drifted past.
The game had grown tedious, Falkirk appearing content to hold their lead as they began to sit deeper and inviting the Fir Park side onto them.
It was a dangerous ploy and one that almost backfired on 80 minutes when Sutton laid off to Porter whose placed shot looked net-bound until Flinders stretched out a hand.
Late home substitute Mark Stewart then quickly saw an on-target shot deflected wide by Mark Reynolds for a corner before Higdon's effort was blocked over from the set-piece.
A frantic Well rally at the death saw Hughes' shot crowded out as the Bairns survived to emerge victorious.