That, added to scores from Charlie Hodgson and Matt Stevens, guaranteed Saracens their first Aviva Premiership match to be played at their new Allianz Park home ended in victory.
And while Vunipola displayed his try-scoring credentials for all to see, McCall admitted he was equally impressive in his bread and butter work.
"I thought Mako Vunipola was magnificent," he said. "He wasn't just good in the loose where he is as good as anybody, he was good in the tight as well. He scrummaged really well today. He's already a special player.
"We had no instruction from England to play him for a certain time and he needed game time.
"We were quite frustrated at half-time. We felt we had created a lot and had clear-cut opportunities which we blew except for one which Charlie took.
"Thankfully we were patient and much more clinical in the second half. To start like that it's great to get four tries at our new home and the players really enjoyed it.
"The pitch feels good and there is a temptation in certain situations where you might kick where it feels right to run.
"Our style is about doing the right thing at the right time so if it's on in our half, we'll go. If it's not we won't. Today we had a lot of ball in hand and broke Exeter down.
"I thought there was nothing to be negative about with the pitch. We didn't have re-set scrums. It was a faster game with more ball in hand than previously."
Exeter head coach Rob Baxter admitted his side were fortunate to go in just 7-3 down at the break but after suffering back-to-back defeats in the Aviva Premiership, he was making no excuses.
"At half-time in reality we shouldn't have been as close as we were," he said.
"I think we were a little bit off in a couple of areas today and when you play a team like Saracens that exacerbates very quickly with anything other than a very high-level performance. It's difficult to know why we were off the pace.
"Maybe the first time on a different surface but I don't want to look for excuses. I just want to roll through it. I've said to the guys you win and lose games in the Premiership.
"Sometimes a game will get away from you and it did. The thing if you have to do against Saracens is keep them under pressure because that's when their game plan can't explode and open up.
"Their individual ball carriers were better than ours as were their individual stop tackles. We had some decent moments and parts of our game went well. But they controlled territory and the breakdown area and that was the making and breaking of the game."
Saracens: Ransom (Maddock, 71); Short, Tomkins, Powell (Mordt, 67), Strettle; Hodgson, De Kock (Wigglesworth, 50); Vunipola (Auterac, 71), Smit (George, 59), Stevens (Du Plessis, 71), Borthwick, Botha (Hargreaves, 55), Wray (Melck, 67), Fraser, Joubert
Exeter Chiefs: Arscott (Dollman, 66); Nowell, Whitten, Shoemark, Jess; Steenson (Mieres, 58), Chudley (Thomas, 40); Moon (Rimmer, 58), Clark (Yeandle, 62), Tui (Brown, 66), Mumm (Hayes, 78), Welch (Muldowney, 66), Baxter, Scaysbrook, Horstmann
Scorers
Saracens
Tries: Hodgson, Stevens, Vunipola 2
Conversions: Hodgson 4
Penalties: Hodgson
Exeter Chiefs
Tries: Baxter
Conversions: Mieres
Penalties: Steenson 2
Yellow Cards: Arscott
Referee: Martin Fox
Attendance: 9,999
