It was initially a struggle for the champions at a sodden Fir Park after Well defender Bevis Mugersgabi opened the scoring in the 13th minute from the tightest of angles.
Rangers huffed and puffed before captain James Tavernier, celebrating his 30th birthday, levelled with a terrific volley in the 43rd minute before crossing for striker Sakala to head the Ibrox men into an interval lead.
The Zambia international added a third with a deflected drive in the 63rd minute before Well captain Stephen O’Donnell was dismissed by referee Nick Walsh for a second yellow card tackle which signalled a rout.
Midfielder Glen Kamara drove in a fourth in the 75th minute and Sakala secured his hat-trick with five minutes remaining before Kemar Roofe made it six in added time to take Steven Gerrard’s side four points clear of Old Firm rivals Celtic.
The pressure that was on Rangers following the 2-2 home draw with Aberdeen in midweek was alleviated to an extent by Celtic’s draw at home to Livingston on Saturday and defeats for Hearts and Dundee United.
Looking to take advantage of the chasing pack’s slip-ups, Gerrard returned Allan McGregor to the goal with midfielders Steven Davis and Scott Arfield and Sakala also drafted in.
Gers midfielder Joe Aribo headed past the far post from close range in the sixth minute when he should have done better but from their first effort on goal, Motherwell scored.
Sondre Solhom Johansen’s header following a needlessly conceded corner was parried by McGregor down at his left-hand post and Mugabi, back in the Well side, was first to react, hammering it into the net from an acute angle.
Kelly made a fine save from Aribo in the 29th minute and then tipped a powerful long-range drive from Alfredo Morelos over the bar for a corner which was again defended.
However, the game took a twist in the final two minutes of the half.
Gers’ left-back Calvin Bassey’s cross from the left was met by Tavernier, who volleyed it low past the helpless Kelly and into the far corner of the net.
Then the Ibrox skipper’s perfect cross into the box from the right was headed in by Sakala to give the visitors the interval lead that had looked so unlikely for so long.
Rangers kept up the pressure in the second half and were rewarded further in the 63rd minute when Sakala’s drive from the edge of the box nicked Motherwell’s Sean Goss and ended up in the net.
It was soon to get more distressing as O’Donnell, booked in the first half for a foul on Sakala, brought down Bassey and took the walk up the tunnel, leaving the Steelmen down to 10 men.
It became a stroll for Rangers in the final stages.
Kamara drove low past Kelly from 25 yards in the 75th minute and 10 minutes later Sakala latched on to a Davis cross to knock the ball past a hesitant Well keeper, who was beaten again in injury time when Roofe, on for Morelos, tapped in from a yard following a Tavernier corner to complete the rout at Fir Park.