Henri Anier's 39th-minute goal was all that separated the teams at the interval, before Ryan Christie brought Caley level with 16 minutes to play.
The hosts' European ambitions, however, suffered a blow when Vigurs scored eight minutes from time against the run of play.
Inverness manager John Hughes was forced to shuffle the pack with Josh Meekings suspended after being sent-off against St Mirren last time out, while Richie Foran (knee) and Aaron Doran (hamstring) remained on the sidelines.
Danny Devine came in to partner Gary Warren in central defence, while Ryan Esson, making his first appearance of the season, and Carl Tremarco were given starts. Dean Brill and Ryan Christie dropped to a six-man bench.
Motherwell made three changes from the side that were beaten 2-1 by Kilmarnock at the weekend.
Anier, Fraser Kerr and Jack Leitch replaced Lionel Ainsworth, Zaine Francis-Angol and Craig Moore, who were all amongst the substitutes.
With both teams looking to enhance their European aspirations, the game started brightly with chances at either end.
Esson had to punch away Vigurs inswinging free-kick, while Graeme Shinnie opted to try his luck from 25 yards with a drive that whistled narrowly past the upright.
Greg Tansey then had an effort from similar distance for Caley as the visitors partially cleared a corner, but it fizzed high over the crossbar.
Both teams were fancying their chances from distance, Craig Reid next to fire one in from 30 yards for Motherwell that stung the palms of Esson.
Neither side were posing a sustained threat in the final third until Kerr's long ball split the home defence, allowing Anier to run through and take a touch before clinically dispatching a low effort from 16 yards into the corner of the net via the inside of the post.
Inverness departed for the dressing room to audible jeers from some of the home support, frustrated by the lack of cutting edge shown by their team.
Motherwell looked content to sit in and soak up the pressure at the beginning of the second half, although Vigurs showed the visiting team were still a threat with a floated free-kick from 25 yards that landed on the roof of the net.
Inverness needed something to provide a spark for them in the final-third and only a fine block by Stephen McManus thwarted Tansey as he pulled the trigger from James Vincent's incisive pass.
Tansey then came even closer moments later, firing one in from 30 yards that had Gunnar Nielsen beaten, but rattled the post before bouncing away to safety.
Just as frustration was beginning to set in, substitute Christie breathed new life into Caley's chances of a victory with 74 minutes gone.
The ball broke to the youngster, a product of the club's youth system, and he struck it sweetly from 25 yards finding the corner of the goal beyond the dive of the despairing Nielsen.
Motherwell had barely been seen as an attacking force in the second half, but they would emerge with the three points courtesy of an 82nd-minute winner.
Devine was somehow left isolated with Vigurs and Craig Moore, who worked several passes between them, before Vigurs finished off the quickfire counter-attack with composed effort from just inside the 18-yard box.