Former England international Charlie Hodgson helped himself to a 16-point haul as Saracens won their first-ever Premiership game at Allianz Park.
Despite being without all their current England contingent, Saracens looked too strong once Hodgson had converted his own try for a 7-3 half-time lead.
Saracens props Mako Vunipola (2) and Matt Stevens shared the home side's three second-half tries between them.
Richard Baxter finally claimed Exeter's only try just three minutes from time.
The Chiefs' other points came from two Gareth Steenson penalties, the first of them to open the scoring on 24 minutes.
It was a rare four-try victory for Sarries, who had run in only 14 in as many games - the lowest try tally in the league.
It was also a ringing endorsement for the artificial pitch at Saracens' new £24m Barnet Copthall home, which was staging its second match but their first in front of a capacity 10,000 crowd.
The only potential cloud hanging over the £500,000 surface designed specifically for rugby union was the place-kicking displays produced by fly-halves Hodgson and Steenson.
Between them they missed six shots at goal before the interval, although normal service resumed for Hodgson in the second half when his sights had been readjusted.
VIEW FROM THE DRESSING ROOM
Saracens director of rugby Mark McCall:
"It's great to start like that, scoring four tries. It was a great atmosphere. We've all been to Vicarage Road over the last couple of years and it wasn't like that.
"There was a real atmosphere during the warm up and the crowd really got behind the team.
"It was a quick game and our players enjoyed it. They were saying in the changing room afterwards that they really enjoyed the experience.
"The pitch feels good and I don't think there was anything to be negative about. We didn't have reset scrums.
"It seemed to a faster game with more ball in hand than previously, so there's a lot to be positive about."
Exeter Chiefs head coach Rob Baxter told BBC Radio Devon:
"We got taught a few lessons, probably about individual physicality.
"We didn't lose every collision and every contact, but I think as a team they just enforced their game plan and physicality on us to a degree that we couldn't handle in the end.
"Their individual ball carriers, their individual workrate started to control the game. Once they controlled territory it was a matter of time before they scored tries.
"We're obviously frustrated but I think the key for us is not to get so desperate that we're hunting for a win, and we don't play in the right manner. The key for us next week is to make sure we play in the right manner and the results will come."
Ransom; Short, J. Tomkins, Powell, Strettle; Hodgson, de Kock; Vunipola, Smit, Stevens; Borthwick, Botha; Wray, Fraser, Joubert.
Maddock for Ransom (71), Mordt for Powell (67), Wigglesworth for de Kock (61), Auterac for Vunipola (71), George for Smit (59), Du Plessis for Stevens (71), Hargreaves for Botha (55), Melck for Wray (67).
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