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Bath got their first Pool A win in the Prem Rugby Cup at Exeter while Saracens crushed Newcastle Red Bulls 54-19 to go top of Pool B.
Fly-half Ciaran Donoghue scored 20 of Bath's points in their 35-19 win at Sandy Park.
His side got off to a great start as Tom Carr-Smith was put in by Sam Winters for a fifth-minute try.
The Blue, Black and Whites dominated the first quarter and doubled their lead thanks to Jack Harrison's score as they played some excellent flowing rugby.
But Exeter got back into the game before half-time as debutant Carwyn Tuipulotu showed his power with two close-range tries either side of a Donoghue penalty as Bath led 17-12 at the break.
Donoghue crossed to extend Bath's lead to 24-12 two minutes after the break as he ran in from 20 metres after a good set play from a scrum.
He added a penalty with 11 minutes to go, but Exeter kept in touch when Sam Harris got on the end of some superb handling to go in under the posts and make it 27-19.
Bath earned a bonus point with a Max Pearce try from a rolling maul with five minutes to go before Donoghue kicked his third penalty as the clock wound down.
It moves Bath up to third place in Pool A while Exeter slip to the foot of the table.
Meanwhile Saracens blew away Newcastle Red Bulls at Allianz Park.
The hosts were 40-0 up at half-time as they ran in six tries and secured their bonus point after just 18 minutes - Eoghan Clarke scored twice after Tom James and Fraser Rawlins had gone over.
Nathan Michelow and Andy Onyeama-Christie crossed in the final 10 minutes of the first half to extend the lead.
Jake Dalziel finally got the Red Bulls on the scoreboard 11 minutes after the break, but Toby Knight and Charlie Bracken's tries extended the lead to 54-7 with eight minutes left.
Red Bulls ended on a high note as Finn Baker and Kaleem Barreto scored tries in the final three minutes but they remain second-from-bottom of their pool.