The result sees Exeter extend their lead at the top of the Premiership to five points over Northampton.
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Exeter began strongly and took a 10th-minute lead when they declined a kickable penalty in favour of an attacking line-out and were rewarded when Vermeulen forced his way over.
Steenson converted but Chiefs bungled the restart to allow the hosts their first period of pressure. It was a sustained one and Gloucester should have taken something from it but they neglected to kick a straightforward penalty in favour of a scrum, and the opportunity was lost when the home pack were shunted backwards.
Eager to back on the horse was our Stuart! https://t.co/V77mdsUZEJ
— RugbyPass (@RugbyPass) February 14, 2020
The Cherry and Whites continued to have the better of the second quarter with two superb lengthy touch-finders from Danny Cipriani keeping Chiefs penned in their own half, but Gloucester could make little headway against a resolute defence so they trailed 7-3 at the interval.
Exeter had the advantage of the wind in the second half and seven minutes into it, they extended their lead when Steenson kicked a 40-metre penalty.
And in the space of the next 12 minutes, the 35-year-old was on target with three further penalties from similar range as Exeter turned the screw in the third quarter.
Trailing 19-3 and looking to reverse their fortunes, Gloucester made four changes to their pack in one swoop but it was to no avail as Exeter sealed victory with the best move of the match.
Hogg started it from inside his own half with an elusive run before the Scotland full-back was on hand to race the final 15 metres to score after skilful inter-passing had created the opportunity.
Steenson kept up his perfect kicking by converting but Gloucester showed spirit in the final 15 minutes and were rewarded with tries from replacement flanker Polledri and wing Rees-Zammit.
– Press Association
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