The Chiefs vaulted Northampton at the summit as flanker Don Armand grabbed a brace of tries, with one each from locks Jannes Kirsten and Jonny Hill, with fly-half Gareth Steenson converting all the touchdowns and also a penalty.
Leicester were in the box seat with a super first-half display as England wing Jonny May went over twice, and flanker Jordan Taufua added another try, while England stand-off George Ford booted two conversions and a penalty.
But it was not to be Leicester’s day, although they gave it a go.
Leicester brought a whole raft of their England World Cup stars back for the match, and they soon made their mark with a barnstorming opening half.
The Tigers, languishing in the bottom two in the Premiership, belied that position as they romped away to a 19-7 lead after just 20 minutes.
Exeter, league runners-up last season, had taken the early lead when Kirsten had driven over near the posts for Steenson to convert.
An attack in the Exeter 22 saw Ford cross-kick, Taufua gather and the big New Zealander run through Exeter full-back Stuart Hogg to score.
And when England centre Manu Tuilagi made hay inside the Exeter half, he sent May off from 20 metres to fall and twist over and touchdown amid a tackle from defending Olly Woodburn.
That made it 19-7 and the Tigers were heading for a bonus point before half-time.
But it did not arrive as Exeter fought back, with Armand touching down under a pile of bodies for Steenson to convert and bright the Chiefs to within five points.
However, an error 26 metres out gave Leicester the chance to increase their lead. Ford obliged with a sumptuous penalty for the teams to turn around with the score 22-14.
The game was delightfully in the balance as Steenson added three more points to the Chiefs total with a 22-metre penalty after the break.
There was not much to choose between them but, after a couple of attacks that the Tigers repelled, Exeter finally went back into the lead as Armand drove over from a metre with Steenson adding the extras.
And moments later, Hill finished off a back move by bouncing Ford out of the way for a corner touchdown that secured Exeter’s bonus point.
The Tigers battled hard to get back into the match as the rain poured down. However, the channels to the touchline were covered by the visitors and Leicester ran out of ideas of how to break down the Chiefs at the end.
The match in pics:
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