The European dream might be over for Motherwell but John Sutton is certain the whole experience will be back on the calendar at Fir Park next season after securing the victory that erased the memory of that Uefa Cup capitulation to AS Nancy.

The striker’s fifth goal of the campaign, a 55th-minute header, decided an entertaining Clydesdale Bank Premier League contest after Falkirk had twice clawed their way back. Sutton revealed later that Mark McGhee, the manager, had fuelled the Motherwell players’ ambitions. “He told us this was the first qualifying game to get back into the Uefa Cup,” Sutton said.

Motherwell were given a helping hand towards the three points by Robert Olejnik, the Falkirk goalkeeper, whose first-half error presented Chris Porter with his first goal of the season. However, John Hughes, the Falkirk manager, refused to hold Olejnik culpable. “We have lost cheap goals all season but I am not going to criticise Robert,” he said. “I felt sorry for him. He is only 20. He should have held on to the ball and just taken a booking for sliding out of the box but everyone makes mistakes.”

Just 12 minutes into the game, Jamie Murphy had underlined his promise with a ruthless finish. The teenager’s local knowledge paid off after Keith Lasley’s long ball veered awkwardly after it sailed over the Falkirk defence. Murphy anticipated the bounce that bemused Jackie McNamara and advanced into the box to steer a finish beyond Olejnik.

Falkirk, though, restored parity by the 21st minute when Steve Lovell displayed equal menace. Tom Scobbie clipped a searching pass down the left flank, which was flicked on by the head of Michael Higdon into the run of Lovell, who drilled a low right-foot shot past Graeme Smith.

However, Falkirk were not able to even savour their celebrations before Motherwell regained the lead with a freak goal. Olejnik sprinted out to gather a long ball but as the goalkeeper’s slide began to take him out of the area he released the ball to ensure he was not punished.

Olejnik clearly thought that Lee Bullen, who had been close by, would mop up behind him but Bullen had turned his back on the action and was unaware that the loose ball was now the property of Porter until the striker thrashed it into the empty net.

At least Olejnik and Bullen both atoned for their errors. Olejnik denied Steven McGarry just before half-time by pawing the midfield player’s fierce shot wide and then Bullen made a clearance off the line from Porter’s downward header.

The value of that moment became clear just four minutes into the second half when Falkirk levelled again. A patient passing move around the edge of the box eventually saw Scott Arfield roll a pass into Graham Barrett, who eschewed the lay-off to Higdon and instead turned Mark Reynolds before firing a right-foot shot past Smith from 12 yards.

Yet, Motherwell are the epitome of resilience and McGhee’s side edged back in front just six minutes later. The industrious Steven McGarry worked so hard to create space to deliver a cross that was perfect for Sutton, who had eluded his marker, to power a firm header into the roof of the net. However, they had to live on their nerves before embracing this victory, It required a great save from Smith to keep out Higdon’s header from Neil McCann’s corner.

Motherwell (4-4-2): G Smith 6 – P Quinn 7, S Craigan 7, M Reynolds 7, S Hammell 6 – J Murphy 7 (sub: D Clarkson, 76min), S Hughes 6, K Lasley 8, S McGarry 8 (sub: M Fitzpatrick, 71) – C Porter 7, J Sutton 7. Substitutes not used: G Nielsen, R Malcolm, J O’Brien, D Smith, K Connolly.

Falkirk (4-4-2): R Olejnik 5 – J McNamara 5 (sub: G Aafjes, 65 6), D Barr 7, L Bullen 4, T Scobbie 6 – G Barrett 7 (sub: R Latapy, 79), S Arfield 7, K McBride 7, B O’Brien 5 (sub: N McCann, 67 4) – S Lovell 7, M Higdon 7. Substitutes not used: S Flinders, P Cregg, M Stewart, S Lynch. Booked: Scobbie, Higdon.