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A teak-tough defence and astute kicking game, aided by Farrell's trusty boot, were key for what turned out to be a comfortable victory at Lyon's Grand Stade although the game will not likely go down in the annals as one of the best spectacles.
Not that Saracens No 8 Billy Vunipola cared.
"It's awesome, we're in that club now! We managed to pull it off. To win this trophy is a massive honour," he told Sky Sports.
"It was such an arm-wrestle. We made less mistakes. Credit to our front five and credit to big Fab (Farrell) for holding his nerve."
Farrell added: "It's a great moment for the club. To be involved in a competition like this and to play teams like Racing... to win this competition is brilliant.
"It's a brilliant achievement. For (captain) Brad (Barritt) now to get to lift this trophy, it's going to be something that everyone remembers."
Skipper Barritt said the players would be free to celebrate on Saturday night before refocusing for the English Premiership semi-final playoffs next weekend.
"I'm hugely proud to be part of an unbelievable club," said Barritt.
"We spoke about pounding the rock and eventually the rock cracked today."
He added: "This is big, this is everything that we've wanted over the past six years. I think everyone has full rein to enjoy it."
All Black legend Carter failed to influence the game in any way, visibly struggling with the pace and contact, and even opting from the off not to kick from the tee. He was replaced three minutes into the second-half, seemingly injured, to little fanfare.
His much-vaunted partnership with in-form France scrumhalf Maxime Machenaud was also short-lived as the France international went off concussed after just 18 minutes.
Both sides struggled to impose any kind of recognisable gameplan, the match at times descending into harum-scarum tactics chasing a slippery ball in midfield and around the fringes of the ruck.
After Montpellier's 26-19 victory over Harlequins in the Challenge Cup on Friday, Racing were seeking a first French double in European competition since 1997 when Brive and Bourgoin triumphed.
Machenaud, handed the kicking duties for Racing, scuffed a first early effort and Saracens replied by mounting the pressure.
Farrell put a dinked kick through and as Chris Ashton went to recover, the covering Brice Dulin dabbed the ball out, handing the English side a scrum five from which they won a penalty, Farrell converting.
As the heavens opened, Barritt put an enormous hit in on Carter, the leading Test points scorer taking his time to get to his feet amid a succession of knock-ons with the slippery ball.
Saracens loosehead Petrus du Plessis was again pinged for collapsing the scrum, South African centre Johan Goosen drawing Racing level with a 55-metre penalty.
Farrell saw an ambitious drop-goal go wide but made no mistake with a second penalty, also getting in another big hit on a shaky-looking Carter after the re-start.
Saracens, who lost 23-6 to Toulon in the 2014 final, managed to pin Racing back effectively through the accurate kicking of Richard Wigglesworth and Alex Goode, and Ashton went close after following through on another Farrell grubber.
The England fly-half extended Saracens' lead with a third penalty just after the half-hour mark, a deficit cut back by Goosen's second after some solid Racing pressure in what was proving to be a tough, tight game.
Farrell held his nerve through whistles and hooters to nail a fourth penalty to hand Saracens a vital 12-6 half-time lead.
After Carter strolled off to be replaced by Remi Tales, Sarries played the percentage game, Wigglesworth and Farrell pinning Racing back although the Parisian club's defence held firm.
The pressure eventually told, however, Farrell landing his fifth penalty as the England trio of prop Mako Vunipola and lock pairing Maro Itoje and George Kruis came to the fore in the loose.
Goosen pulled one back for Racing after a series of well-organised pick-and-go's, but Farrell deservedly had the last word with his sixth and seventh penalties to seal Saracens' first European title having not lost a game in this season's competition.
Winners of the European Champions Cup after Saracens beat Racing 21-9 at Lyon's Grand Stade on Saturday:
2016 - Saracens (ENG) 21 Racing 92 (FRA) 9
2015 - Toulon (FRA) 24 Clermont (FRA) 18
2014 - Toulon (FRA) 23 Saracens (ENG) 6
2013 - Toulon (FRA) 16 Clermont (FRA) 15
2012 - Leinster (IRL) 42 Ulster (IRL) 14
2011 - Leinster (IRL) 33 Northampton (ENG) 22
2010 - Toulouse (FRA) 21 Biarritz (FRA) 19
2009 - Leinster (IRL) 19 Leicester (ENG) 16
2008 - Munster (IRL) 16 Toulouse (FRA) 13
2007 - Wasps (ENG) 25 Leicester (ENG) 9
2006 - Munster (IRL) 23 Biarritz (FRA) 19
2005 - Toulouse (FRA) 18 Stade Francais (FRA) 12
2004 - Wasps (ENG) 27 Toulouse (FRA) 20
2003 - Toulouse (FRA) 22 Perpignan (FRA) 17
2002 - Leicester (ENG) 15 Munster (IRL) 9
2001 - Leicester (ENG) 34 Stade Francais (FRA) 30
2000 - Northampton (ENG) 9 Munster (IRL) 8
1999 - Ulster (IRL) 21 Colomier (FRA) 6
1998 - Bath (ENG) 19 Brive (FRA) 18
1997 - Brive (FRA) 28 Leicester (ENG) 9
1996 - Toulouse (FRA) 21 Cardiff (WAL) 18
