Aviva Premiership leaders Saracens were made to fight tooth and nail for a 23-17 opening win in the Heineken Cup, needing a late Owen Farrell penalty to edge past a hugely determined Connacht side.
A brace of penalties from Farrell were the only scores of a defence-dominated second half at the Sportsground, as 8/1 outsiders Connacht - inspired by man of the match Kieran Marmion - stayed in the hunt for a shock victory.
They almost got it right at the death as bodies piled in close to the Sarries line, but replacements Aly Muldowney and Paul O'Donohoe were held up short and the relieved visitors got out of Galway with the points.
But, despite a further penalty from Farrell, Mark McCall's men were reeled in by half-time.
Scrum-half Marmion and Danie Poolman both touched down with the latter's score - converted by Dan Parks - getting Connacht back level at 17-17.
A second Farrell penalty put the visitors ahead again in the 53rd minute and the England and Lions fly-half decisively added his fifth successful kick of the night with five minutes to go.
Quarter-final and semi-final appearances in successive seasons have certainly whetted Sarries' appetite for European success and they laid down an early marker here with Wyles and Ashton's scores.
United States international Wyles scorched home for the sixth-minute opener, following some smart link-up play between Farrell and David Strettle straight from a lineout. With his centre partner Joel Tomkins running the decoy, Wyles was set free and he showed good pace to finish off with Farrell converting.
Connacht, wearing an all-black strip, respond through the boot of Parks, who swung a difficult penalty over from the right. However, the power-packed visitors put the pressure back on from the restart.
McCall's side gave evidence of their expansive ability as backs and forwards suddenly flooded forward, including the strong-carrying Mako Vunipola. His front-row colleague Schalk Brits was standing wide on the right to put Ashton over for a neat finish in the corner.
Farrell's crisp conversion widened the gap to 11 points - just reward for Sarries' high level of execution and the control shown by half-backs Farrell and Neil de Kock.
But their Connacht counterparts, Parks and Marmion, drove the province back into the game in the second quarter, with the hosts also tightening up their defence after some costly missed tackles.
Poolman did well to hare after a high kick and Marmion profited, collecting the ball out wide and cutting through from the left for an opportunist 18th-minute try. Parks tapped over the simple conversion.
Sarries answered back with a long-range Farrell penalty but Connacht exerted more control approaching the break.
Their forwards grew in stature and a spell of patient build-up play was rewarded just past the hour mark when South African Poolman stepped inside two defenders to score, with quick passes from John Muldoon and Marmion creating the chance.
Parks converted but missed a late penalty as the sides went in all square, and Saracens regrouped to force the issue on the resumption with George Kruis and scrum-half De Kock both going close.
George Naoupu leaked a penalty near the Connacht line which allowed Farrell to boot his side back in front, but the hosts' gritty defence continued to frustrate Sarries.
After conceding a huge amount of territory, heroic Connacht had their opportunity to build from a penalty far out and their forwards probed before Saracens won a scrum and eventually cleared from their 22.
The game remained in the balance as Farrell flicked a drop goal effort wide, however Saracens did enough to claim a tight six-point verdict in the end - the key moment seeing a Steve Borthwick-led maul set up Farrell's match-winning penalty.