Sherwin Seedorf sent Stephen Robinson's team on their way to all three points when he opened the scoring in the first half as he grabbed his first league goal.
After the interval Well ran over the top of Hibs to cruise to the win following a Liam Donnelly penalty, following an Adam Jackson handball, and strike from substitute Jermaine Hylton.
Motherwell thoroughly deserved the win and the nature of this defeat was too much for some of the Hibs fans to bear as section of the travelling support called for manager Paul Heckingbottom to be sacked.
Both of these sides had an identical record going into this league clash: a win, a draw and a defeat apiece from their three opening Premiership games.
Hibs were first to threaten when Flo Kamberi had a drive beaten away by Motherwell goalkeeper Mark Gillespie.
Motherwell should have opened the scoring when James Scott slid a pass to Christopher Long inside the penalty area but the striker hesitated and was unconvincing with his finish as Ofir Marciano saved his effort.
Gillespie pulled off another impressive stop when he turned Stevie Mallan's 25-yard free-kick round a post.
Motherwell then threatened when Liam Polworth slid a through ball to Seedorf but his shot was deflected over.
From the resultant corner Jake Carroll drilled in a low ball that Long, who had darted to the near post, got on the end of - but he could not steer his shot on target.
Motherwell went ahead after 23 minutes as Seedorf finished off a rapid counter-attack.
Gillespie denied Glenn Middleston and then launched an attack and when Seedorf picked up possession on the left flank he then cut in-field and darted past Steven Whittaker to drill a right-footed shot into the far corner past Marciano.
Motherwell came close to a second when Seedorf beat Whitaker once again inside the penalty area and then cut back for Scott, but the 19-year-old fired over.
The home side continued to push for a second after the interval and came close to it when Declan Gallagher's downward header from a Polworth corner was saved by Marciano, but as he scooped the ball clear it came to Long, who diverted his header over.
Long then had another chance when he broke in behind the Hibs defence but once again he was denied by the Hibs goalkeeper.
Hibs defender Adam Jackson spurned a great chance to equalise when the ball broke to him inside the box but from 12 yards out he drilled his shot straight at Gillespie.
Jackson's afternoon then got worse when he conceded a penalty with 12 minutes remaining as he blatantly handled Gallagher's header from a Polworth corner.
Referee Steven McLean rightly pointed to the spot and Donnelly made no mistake as he sent Marciano the wrong way to notch his eighth goal of the season.
It got even better for Well as, in the 86th minute, Hylton got on the scoresheet as he lashed a shot beyond Marciano.