Vigurs' crisply taken, superbly worked winner created a single-point cushion to Aberdeen, although there remains everything to play for with Derek McInnes' side now holding one game in hand.
For Inverness, defeat marked a terminal blow in their own European ambitions, as they sank 10 points off third place amid a poor streak of just one win in nine games.
There was some solace for the hosts in young prospect Ryan Christie's brilliant finish, but concern at defensive frailties in an otherwise pretty even encounter. "We have a lot of injuries but I've told the lads they'll get all the rest they want in the summer," said Stuart McCall, the Motherwell manager, acknowledging his jaded "walking wounded".
"We have six games to go and there's a month or something left. It's going to take a massive effort from everyone to get over the line. This isn't the time of year for rest, this is the time to keep going and these lads will do that."
John Hughes had billed this as a "must-win" occasion for his side, given dwindling European aspirations, but he had to tackle it without the considerable influence of injured captain Richie Foran. With Aaron Doran's trickery also consigned to the treatment table and central defender Josh Meekings suspended, Hughes made three changes and could muster only six substitutes.
Motherwell had lost here 2-0 back in August but won by the same scoreline a fortnight ago at Fir Park. McCall, also making three changes, knew victory would knock one of his Europa League rivals out of the running. James McFadden was the most notable of five absences for the third top side.
The hosts' need was probably greater, given the points chasm between them and the visitors, and they certainly displayed the greater urgency in the early exchanges.
Vigurs' free kick from the right did force an early punched save from Ryan Esson, but the home side went closest after 13 minutes. After a rapid break, Shinnie boldly went for goal, 25 yards out, and his curling attempt rippled the side-netting at pace.
The tempo and tackling was keen and competitive, but, with indecent haste, a section of the home crowd in the main stand were all too soon on the players' backs.
Motherwell - backed by barely a few dozen hardy fans - were patient, biding their time and never committing too many men forward.
Sure enough, McCall's men hit clinically on the break to take the lead. Fraser Kerr deserved credit for spotting the chance to spear a long through pass from deep into the path of Henri Anier. The Estonian striker's turn of pace took him free of the home defence and he dinked a cool shot past the outcoming Esson for his eighth goal of the season.
The away side continued to play it canny, soaking up pressure and picking their moment to break, while the home side kept grafting, working the ball with purpose but still with a vocal, critical element of the support on their backs.
Hughes introduced the more attack-minded Christie for fellow 19-year-old Liam Polworth just after the hour in an obvious attempt to up the attacking ante. Two minutes later, Stephen McManus had to make a timely sliding block to keep out Greg Tansey's fierce strike at an angle on the right side of the box after a superbly-picked pass by James Vincent. Then, Tansey again threatened, catching a 30-yard strike with ferocious power, rattling the inside of the right-hand post almost out of its foundation.
There was no dubiety in Hughes' intent at all. After 67 minutes the attack-minded Marley Watkins replaced home full-back David Raven.
Motherwell, though, consistently drew eight or nine men deep when the hosts held possession, expertly snuffing out the home movement and intent. It was going to take something extra special to turn the tide and, to the delight of the Highland support, so it arrived.
When it seemed as if they had, again, smacked square into a wall of claret and amber, the ball broke to young Christie 25 yards out.
The son of past club great Charlie, touted for young Scotland international recognition this week by his manager, took a neat touch and unleashed a quite brilliant strike low past Gunnar Nielsen.
Suddenly, there was an onus on McCall's men to be more expansive with the points again in the balance.
But, with not long to go, the familiar figure of Vigurs exposed the home defence. He and substitute Craig Moore wove their way through the middle, exchanging several passes with each other before the former expertly cut a shot beyond Esson's despairing dive.
There were howls for a home free kick to the right of the box moments after the restart but referee Craig Thomson waved play on and Tansey drove across the face of goal with no takers. "It's just very disappointing as the other teams are drawing away from us," Hughes had to acknowledge after the game.
"I've seen the goals and it is something we've touched on and eluded to but we give teams too much time. Did we deserve something out of the match? Yes we did."