A third Luis Suarez goal in as many games helped Liverpool book a place in the third round of the League Cup, as Exeter were comfortably seen off at St. James' Park.
A Daniel Nardiello penalty handed Exeter some consolation for their efforts, but Dalglish's 200th win in all competitions as Liverpool manager means that it will be his side progressing further in the competition.
With the Reds being starved of European competition in 2011-12, it's no surprise that competitions like the League Cup are to be taken very seriously, with a very strong line-up (featuring the likes of Jose Manuel Reina, Charlie Adam, Martin Skrtel, Suarez and Raul Meireles) taking to the field.
A great atmosphere greeted the two sides, who were separated by 60 places in terms of league football, but Liverpool could have dampened the good mood on just 10 minutes. Adam's short corner led to the Scot finding himself free in the Exeter penalty area. His near-post effort was forced behind by 'keeper Artur Krysiak.
The hosts showed glimpses of what they could offer to the evening, with an unmarked Nardiello heading into the arms of Reina, just before Raul Meireles' involvement in the match was cut short due to a shoulder injury.
Liverpool took the lead midway through the first half. An incisive counter attack saw Rodriguez free Jordan Henderson on the right-hand side. His cross proved too high to fully deal with for Krysiak, who could only claw it into the path of the on-hand-to-score Suarez.
In between the opener and the interval, the visitors' superiority was on show, with Rodriguez and Adam coming close to doubling the lead. Suarez wasn't letting up; his deft chip in first half stoppage time providing the travelling supporters with plenty to be happy about.
The failure to take such chances almost punished the Merseyside outfit just moments into the second half though, as Nardiello's attempted lob of Reina nearly went in. Despite the effort evading the Spanish goalkeeper, it lacked the power or the accuracy to hand Exeter an unlikely equaliser.
And the hosts' chances of a comeback were ruined when Rodriguez doubled Liverpool's advantage on 55 minutes. Having collected Henderson's pass, Suarez advanced into the area and eventually slipped a ball across the face of goal and into the path of the Argentinean, who dispatched with ease.
Two was soon three. Andy Carroll ended the visitors' scoring with a powerful effort from the edge of the box. It was the January acquisition's first goal of the new campaign. Suarez, who again played a part in the goal, was replaced by Stewart Downing during the celebrations. His departure prompted a standing ovation from both sets of supporters.
Downing almost made an immediate impact, cutting in from the right and forcing Krysiak into a smart save. Carroll headed wide from the resulting corner.
Exeter were handed a chance to reduce the damage in the final ten minutes, as Skrtel brought down Nardiello in the box. The former Manchester United trainee stepped up to fire home a 'souvenir goal' for the home side, but it was Liverpool that advanced into the next round.