Forwards Harry Wells and Jasper Wiese both notched tries for the Premiership club at Twickenham, only for former Springbok fly-half Johannes Goosen’s subsequent score 20 minutes from time to prove decisive in a tense one-point 18-17 triumph for their Top 14 counterparts following an earlier effort from France international wing Vincent Rattez.
Philippe Saint-Andre’s Montpellier - who currently sit 10th in the Top 14 - also got 10 points from the boot of Benoit Paillaugue as they claimed success in European rugby union’s secondary club competition for the second time, following an initial triumph over Harlequins in 2016.
As for Tigers, who were hoping to match the recent exploits of first-time FA Cup winners Leicester City in London in front of 10,000 returning fans at the home of English rugby, their 19-year wait for more European glory goes on despite an impressive bounce-back season under head coach Steve Borthwick.
Their last major trophy of any kind came back in 2013, when they last won the English Premiership.
“We haven’t been in a final for eight years, but we got here and we feel like we’ve moved forward a lot,” Tigers captain and former England hooker Tom Youngs told BT Sport.
“But we came here to win of course and I felt like everyone gave everything they had out there. We’ll learn from this and we’ll keep going.
“Everyone knows what we’ve been through in recent years as a club and there were some young boys out there tonight who will grow immensely from this experience.
“I just couldn’t be prouder of how we’ve got here and it was great to hear a crowd tonight too, they were amazing.”
Montpellier match-winner Goosen said: “We're very pleased to work really hard in a tough season and come away with a trophy.
"It means a lot to all of the guys. I think we've got a hell of a group here who work very hard so it's awesome to win this.
"We tried to approach this one by playing with no fear and the forwards put in a great shift tonight to see us home."
The European Rugby Champions Cup Final also takes place at Twickenham on Saturday night with an all-French affair between Top 14 title contenders La Rochelle - coached by former Ireland and Lions fly-half Ronan O’Gara - and Toulouse.