Ephraim, who was snapped up on a 28-day deal from QPR on Friday, had a hand in both goals while Mendez-Laing climbed off the bench to score for the second time this season.
Posh finally made a breakthrough in the 72nd minute when Ephraim fed Mark Little to deliver for record signing Britt Assombalonga to tap in his first goal in 10 games.
And Posh, who ditched their regular midfield diamond in favour of a 3-5-2 formation, quickly clinched their passage as Ephraim cleverly slipped in Mendez-Laing seven minutes later.
Assombalonga dragged two other excellent opportunities wide as Posh took control in the final quarter of the game while Krysiak was forced into a super reaction save to claw away a deflected Little effort.
Posh goalkeeper Bobby Olejnik was a spectator for much of the afternoon as Exeter offered virtually nothing in attack.
Olejnik wasn't called upon to make a save until former Posh man Arron Davies unleashed a low drive from 25 yards late on.
Ferguson said: "The substitutions made a big difference. They gave us that bit of quality in the final third that we have been missing.
"Hogan will certainly suit the way we played and young Mendez cannot be happy with me because he is regularly making an impact from the bench and not getting a start.
"We seem to have a problem with everyone expecting us to win 8-0 all the time and it doesn't work like that.
"We had to be patient against a good Exeter team in the first half. We had a lot more energy about our performance in the second half and the first goal gave the lads a lift."
- Sports & Recreation
- Hogan Ephraim