After Tom Taiwo had headed Hibs into the lead, Michael Higdon and James McFadden responded with goals early in the second half before Kallum Higginbotham added an excellent third and Tom Hately completed the scoring six minutes from time.
The win takes second place 'Well onto 50 points while Hibs now face the threat of finishing the season in the bottom half of the table.
Visiting keeper Ben Williams had to survive a nervous start to the game, with Motherwell twice coming close inside the opening 12 minutes.
First, Henrik Ojamaa's low shot towards the near post almost proved embarrassing for Williams who failed to hold on to the ball and needed a defender to clear the danger.
And Williams escaped again a few minutes later when he managed to block a curling, dipping free-kick by Hately - which bounced off the keeper's right leg - but Shaun Hutchison was unable to convert the rebound.
Yet, it was Hibs who took the lead against the run of play on 23 when David Wotherspoon's cross was glanced home from 12 yards by the unmarked Taiwo.
Hibs almost added a second five minutes later as James McPake headed inches wide from Leigh Griffiths's corner before Hately missed a glorious chance to equalise on 38.
The defender raced clear only to drag his shot across the front of goal from 10 yards.
However, Motherwell were deservedly level with their first real attack of the second half, when McFadden's chipped cross was headed home from close range by the imposing figure of Michael Higdon.
And, with 53 minutes on the clock, McFadden's left-foot fired Motherwell ahead, as the former Everton striker skipped past three defenders before finding the bottom left-hand corner of the net from 18 yards.
Higginbotham sealed the points midway through the second half with a spectacular 18-yard scissor-kick from Stewart Carswell's cross.
With time running out the influential McFadden found Hately whose firm shot from 20 yards clipped McPake and beyond the reach of the helpless Williams.
Williams did deny Motherwell a fifth goal in the final minute, as he made a brilliant point blank save from Carswell, but Motherwell ran out comfortable winners.