The Uruguayan grabbed the opener after 23 minutes as he volleyed home, before teeing up Maxi Rodriguez and substitute Andy Carroll to put a seal on the victory after the break.
But there was some concern for Dalglish as the Scot lost Raul Meireles to injury inside the first quarter of the game. The Portuguese left the field clutching his shoulder after coming off worse in a challenge with Danny Coles.
Exeter battled bravely but carved out very few opportunities, although Daniel Nardiello did at least pull a goal back from the spot after he had been felled by Martin Skrtel in the box.
Dalglish named a strong side for his first League Cup tie as Reds boss since 1990.
The Grecians may have had dreams of a famous upset but Liverpool were always in control after making an assured start.
Skrtel volleyed into the side netting inside three minutes before Adam forced Artur Krysiak into a near-post save after he was left free at a short corner.
Exeter had a great chance to take a 16th-minute lead as Nardiello was left unmarked from a Chris Shephard corner, but the striker's header was straight at Reina.
Liverpool then lost Meireles to injury after 19 minutes, the Portuguese disappearing straight down the tunnel with Andy Carroll his replacement.
But the Reds overcame that loss and were soon ahead as Krysiak succeeded in tipping a Henderson cross only as far as Suarez, who volleyed home despite the best efforts of Richard Duffy on the line.
Exeter then lost a man of their own as an apparent hamstring injury ended Guillem Bauza's night, with Jimmy Keohane being summoned from the bench.
Rodriguez should have doubled the Reds' advantage after 34 minutes when Suarez turned Billy Jones, but the Argentinian could not get a touch as the ball was rolled across the six-yard box.
Adam then dragged wide from the edge of the box after more promising link-up work between Suarez and Carroll.
Exeter created their second clear chance of the night within seconds of the restart as a Shephard ball saw Nardiello loft the ball over the onrushing Reina, but his effort ran wide of the left-hand post.
Henderson was then booked as he was adjudged to have dived in the area under the challenge of Coles, but the second Liverpool goal arrived just nine minutes into the second half as the ever-threatening Suarez calmly picked out Rodriguez at the second attempt to allow the midfielder to slot into the left-hand corner.
And the win was secured just four minutes later as Suarez beat Troy Archibald-Henville before Carroll smashed an unstoppable left-foot drive beyond Krysiak.
That was the final act in a Suarez masterclass and he was withdrawn with Stewart Downing coming on.
Carroll wasted a good chance to grab his second as he nodded wide but it was Exeter who grabbed a consolation goal with 10 minutes to play.
Skrtel was guilty of a clumsy challenge on Nardiello as the striker broke into the box, and the former Blackpool forward slotted home from the spot.