Luis Suarez got the first goal and then set up Maxi Rodriguez and Andy Carroll for the others before Daniel Nardiello grabbed a late penalty for the hosts.
Liverpool's line-up suggested Kenny Dalglish is taking the competition seriously, but it also served as another chance for his new signings to get experience together.
"I think you've seen with the players out there tonight that we've come here to do a job and we've done that," the former Blackpool midfielder told Sky Sports.
"It's going to be a difficult game coming down here but we've shown the right respect to Exeter, a good side, but done the job and that's the important thing for us.
"We've got good players who can play with each other. That's two wins on the bounce now and we'll look for another on Saturday."
Dalglish was happy to see his new signings take another step forward but was most impressed by the attitude shown against lower league opposition.
"Definitely it gets us another game and the longer they play together and train together the better they'll get, but the most commendable thing is the attitude," he said.
The only bad point for Liverpool was an injury to Raul Meireles, with Dalglish confirming he had damaged his collar bone, although the precise nature of the injury is not yet known.
"He'll come back up with us and we'll see how long it takes," Dalglish said.
"I don't know how serious it is, but it'll be a few weeks."