The supremely-entertaining showpiece finale didn’t disappoint as Henry Trinder and Mark Atkinson’s first-half tries for Gloucester helped them build a 20-6 half-time lead, outdoing Jarrod Evans’ two penalties.
But Tomos Williams struck after the break, Gloucester responded through James Hanson, Garyn Smith and Blaine Scully then bringing the Blues within two points with two minutes left to play.
Anscombe held his nerve to kick the winning penalty from the touchline right at the death, sealing a first European trophy for the club since 2010.
The match in the Basque Country started well for the Blues as Josh Navidi , in his trademark style, locked on to a tackled opponent to win a penalty at the breakdown, which Evans duly swept through the posts.
Minutes later though Gloucester’s Tom Marshall chipped down the line and from the next play fly-half Billy Burns deliverd a sublime cross-field kick for Trinder to touch down in the corner.
Billy Twelvetrees added the extras and on 13 minutes wing Blaine Scully say his try in the corner ruled out for a foot in touch.
Evans notched his second penalty on 16 minutes and then survived a scare just before the half-hour mark as Lewis Ludlow crossed the whitewash but saw the score ruled out for a forward pass.
The English side’s second try came just before the interval as Trinder broke down the left, passed inside to Callum Braley, who in turn fed Atkinson to touch down.
The Blues trailed 20-6 at the break but scored a wonderful try immediately after it, with Anscombe twice chipping through and Williams showing his strength to touch down the ball next to the posts.
Evans made it 20-16 with his third penalty and then the Blues retook the lead as Rey Lee-Lo broke through midfield, Evans grubbered through and replacement Smith touched down the ball.
Evans added the conversion but then the match swung again just before the hour-mark as Hanson muscled over the line from the back of a maul.
Twelvetrees converted and then added a further penalty to create a 30-23 lead as the crowd feasted on a see-saw match.
The best was yet to come.
Danny Wilson’s team weren’t done as play headed into the final minutes with the forwards first driving close to the line and then Matthew Morgan almost dancing his way over.
The attacking pressure eventually told, with Scully sliding over in the corner before Anscombe missed the conversion with the scoreline at 30-28 with two minutes left on the clock.
The Blues held their nerve though and following a break down the left Smith chipped forward and then forced a penalty for holding on, with Anscombe firing the ball through the posts from out wide in the pressure kick of all pressure kicks.
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