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.
It wasn’t all smooth sailing for Liverpool though as Raul Meireles went off injured, inside the first quarter of the game, clutching his shoulder after coming off worse in a challenge with Danny Coles.
With four Premier League clubs going out of the competition on Tuesday, Dalglish was determined not to add Liverpool to that list as his line-up included Suarez, Henderson, Adam and Reina.
Dalglish named a strong side for his first League Cup tie as Reds boss since 1990.
Suarez led the attack having been on bench duty against Arsenal, while Jordan Henderson, Charlie Adam and Pepe Reina were all retained from the side that started against the Gunners.
The Reds went ahead when 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.
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.
Finally though nine minutes into the second half the second Liverpool goal arrived when 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.
All in all a good win. Nice to see Andy Carroll get a goal and that is three in three games for Suarez.