Motherwell will play Europa Conference League football next season after a 2-1 win over Hearts secured a top five Premiership finish.
Joe Efford put the home side into an early lead but the Jambos responded rapidly through Josh Ginnelly, as they created plenty of attacking chances.
'Well's scorer should have turned provider for Sean Goss mere minutes before the interval but opted to go solo and missed, with his teammate staring down an open goal.
Ricki Lamie made up for that moment by scrambling the ball home in the second half to ensure that the club would participate abroad this summer.
They sit fourth and one place below Robbie Neilson's team in third ahead of the final day against Celtic.
Alexander had players struggling with a bug during Saturday's win against Ross County and it struck more of his men ahead of kick-off, but they made just two changes.
Midfielders Mark O'Hara and Ross Tierney dropped out with Callum Slattery and Dean Cornelius coming in. Jambos number one Craig Gordon was rested and replaced by ex-Well goalkeeper Ross Stewart getting a rare start.
That narrow 1-0 success at Dingwall meant the Steelmen knew a win and dropped points for Ross County at Rangers meant guaranteed Europa Conference League football next season and a top five finish.
Given the Staggies found themselves 2-0 down inside the opening 30 minutes in their contest, 'Well knew it was all there in front of them.
It couldn't have started much better as Connor Shields' shot was weakly palmed by Stewart into the path of Efford, who applied the simple task of rolling the ball into an empty net after two minutes.
It was a raucous atmosphere inside Fir Park with what was at stake, and the fact it was club legend and assistant manager Keith Lasley's final match before becoming St Mirren's chief operating officer.
Parity was restored seven minutes later as Juhani Ojala's loose header allowed Ginnelly to surge past him and finish with aplomb beyond keeper Liam Kelly.
After that it was Hearts dominating the attacking chances and Kelly was called upon to make important saves, saving from Ginnelly again on 12 minutes.
Liam Boyce was next to have a go on 18 minutes but another strong save by the home keeper was needed, as 'Well got in at half-time level.
An ill Kevin Van Veen rose from the bench on Saturday to score the winner and he was brought on at the interval in an attacking change by Alexander.
The front three combined instantly and Efford came close to heading home a Shields cross after the Dutchman's dummy run on 47 minutes. Andy Halliday won a free-kick at the other end a few moments later but it sailed wide.
Motherwell had looked more lively in the second period and they got their rewards on 55 minutes. Callum Slattery's corner caused chaos in the box and Lamie popped up with the touch to guide the ball home.
Having signed a pre-contract with Dundee, it was on course to be a fitting farewell for the versatile defender. But Hearts were Scotland's third-best team for a reason so 'Well had to be on their guard.
The game lulled in attack but this suited a home side who didn't need to push forward, rather hold on for a continental prize. Toby Sibbick's injury meant a lengthy amount of stoppage time was to be played.
It led to a nervy Fir Park but already there were beach balls inflated in the home end as a European place beckoned. And sure enough it did as the Steelmen got over the line to send the club back to the continent.
Motherwell: Kelly, O'Donnell, Ojala (Van Veen, 45), Lamie, Carroll, Cornelius, Goss (Tierney, 69), Donnelly, Slattery (Shaw 69), Shields, Efford.
Substitutes: Connelly, Mugabi, Woolery, Shaw, Tierney, Nirennold, Campbell, Mahon.
Booked: Slattery
Hearts: Stewart, Sibbick, Cochrane, Moore, Halliday, Atkinson, Haring, Mackay-Steven, Woodburn (Thomas, 80), Ginnelly, Boyce.
Substitutes: Gordon, Smith, Kingsley, Souttar, McEneff, Devlin, Simms, Tait.
Referee: Matthew MacDermid
Attendance: 5769
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