Ephraim, who arrived from QPR on Friday, was sent on at half-time after a lacklustre opening 45 minutes from Darren Ferguson's team.
The 25 year-old was involved in the build-up as record-signing Britt Assombalonga fired Posh ahead in the 72nd minute.
Assombalonga could hardly miss from point-blank range as he ended a seven-week goal drought after being picked out by Mark Little's delightful low delivery.
And Posh's passage was secured seven minutes later when Ephraim stylishly slipped the ball through to fellow interval arrival Nathaniel Mendez Laing, who fired past Exeter keeper Artur Krysiak.
Assombalonga dragged two other excellent opportunities wide as Posh took control in the final quarter of the game while only some smart Krysiak reactions prevented a wickedly-deflected Little effort from looping in.
Posh goalkeeper Bobby Olejnik was a virtual spectator as the visitors posed next-to-no attacking threat.
Former Posh man Arron Davies did force him into a late save with a low drive from 25 yards.