Liverpool eased into the third round of the Carling Cup with a routine 3-1 win over League One side Exeter City on Wednesday evening.
Luis Suarez was irrepressible once again, scoring one before assisting further second half strikes from Rodriguez and Carroll.
Daniel Nardiello scored a late penalty for Exeter after he was brought down by Martin Skrtel but the Grecians never looked like halting Kenny Dalglish from claiming his 200th win as Liverpool manager.
"We want to win games and the more we win, the harder we will be to beat," Dalglish told reporters after the game. "We will treat the Carling Cup like any other game. The next one is a league match against Bolton, but we will be totally committed and focused to try and win that."
The Reds dominanted from that start, as Dalglish named a surprisingly strong XI at St James Park, including Pepe Reina, Suarez, Charlie Adam, Jordan Henderson and Raul Meireles.
The visitors took the lead when goalkeeper Artur Krysiak failed to hold Jordan Henderson's cross and Suarez was on hand to sweep home the loose ball.
Maxi Rodriguez tucked away Liverpool's second after a Suarez cut-back before a booming strike from Carroll made it 3-0.
Dalglish's night was tempered by an injury to Raul Meireles, who was replaced by Carroll after 26 minutes after he sustained a shoulder injury in a challenge with Danny Coles.
"Raul has hurt his collarbone," Dalglish confirmed. "I don't know what the technical term is but he fell heavily.
"He will come back with us and we will see how long it is before he is back.
"We don't know how serious it is but it'll be a few weeks."