Isaiah Osbourne fired Hibs into a half-time lead at Fir Park, before Higdon (penalty) and Jamie Murphy put the hosts ahead - only for the visitors to respond immediately through Matt Doherty.
Motherwell took the lead for the second time through a wonderful overhead kick from Higdon on 70 minutes and the Englishman then added his third from penalty spot five minutes later.
Ivan Sproule blasted Hibs' third beyond Darren Randolph after the home side had failed to deal with Francomb's corner but it was too little too late.
Omar Daley replaced the suspended Keith Lasley for Well, while top scorer Garry O'Connor was recalled by Hibernian after the 5-0 defeat at home to Celtic.
Manager Pat Fenlon made three further changes with Lewis Stevenson, George Francomb and Sproule returning in place of Pa Kujabi, David Wotherspoon and Eoin Doyle.
Leigh Griffiths fired wide in the opening minute for Hibernian before Daley lashed the ball across the face of Graham Stack's goal at the other end after robbing Doherty.
After Doherty did well to block Higdon's drive, Hibernian opened the scoring after 17 minutes. Tim Clancy's short headed backpass was intercepted by Griffiths, who charged forward and cut the ball back for Osbourne to blast into the net.
Higdon had a weak header comfortably gathered by Stack as the hosts tried to find a way back into the game and Motherwell's leading scorer was denied again two minutes later when James McPake blocked his goal-bound header.
Higdon was a constant threat to the Hibernian defence and he forced Stack into a smart low stop after connecting with Daley's looping cross just after the half-hour mark.
Stack did well to keep out Daley's shot two minutes later and despite being well placed, Murphy could not divert the rebound goalwards.
Osbourne almost added his second of the night when his charging run ended with a powerful effort that ended inches wide, before Daley shot well over as the first half came to an end.
Motherwell were awarded a penalty two minutes after the restart when Henrik Ojamaa seized upon Jorge Claros' header, only to be upended by Stack. Higdon despatched the kick low into the left-hand corner.
Ojamaa was booked for striking the ball beyond Stack after referee Steven McLean had blown for a foul on 53 minutes, despite furious protests from the Estonian that he did not hear the whistle.
Only a brilliant block by Darren Randolph at the feet of Griffiths prevented Hibs from restoring their lead - but in the 63rd minute it was 2-1 to Well when Murphy slid in at the back post to turn Daley's cross beyond Stack.
The visitors levelled almost immediately when Doherty blasted past Randolph after the Motherwell defence had failed to clear Griffiths' corner.
Following the Hibernian equaliser Stuart McCall removed the tiring Daley and replaced him with Chris Humphrey. The visitors made a change of their own when Martin Scott came on for Claros.
Four minutes after being pegged back Motherwell restored their lead in style. Stack denied Ojamaa, but when Murphy chipped the ball back into the penalty area Higdon unleashed a wonderful overhead kick that left the Hibernian stopper helpless.
Higdon made it 4-2 in the 75th minute, completing his hat-trick from the spot after Doherty brought down the onrushing Ojamaa.
Hibernian made a double switch with 10 minutes remaining, introducing Roy O'Donovan and Kujabi for Doherty and Griffiths.
As the hosts tried to wind the clock down Murphy was replaced by Stuart Carswell on 83 minutes.
Clancy's wild backpass almost caught out Randolph and the Irish goalkeeper had to tip the ball behind for a corner.
The visitors dragged themselves back into the game five minutes from time when Sproule drilled home after Francomb's corner had caused problems for the Motherwell defence - but the hosts held on.