The hosts missed a penalty in the first half, with goalkeeper Jonas Lossl saving from Mohamed Salah after captain Tommy Smith was cautioned for pulling Firmino's shirt.
It was a different story after the break, as Sturridge finished clinically following a mistake by Smith, Firmino headed home a James Milner corner and Wijnaldum fired in the third.
Manager Jurgen Klopp named Dejan Lovren in his starting lineup despite having substituted the defender after just 31 minutes during an error-strewn performance against Tottenham Hotspur last time out.
However, the Croatian did not make it to kick-off, picking up an injury in the warm-up and being replaced by Ragnar Klavan, as confirmed by the club's Twitter account:
The late change may have added to the sense of nervousness around Anfield, and the first half was a tame affair with chances at a premium.
The Reds lacked the creativity and invention of Philippe Coutinho but were handed a glorious chance to open the scoring just before half-time.
Smith had a tug at Firmino's shirt in the penalty area, and referee Kevin Friend was quick to point to the spot. Up stepped Salah, but his kick was saved by Lossl, and Jordan Henderson could not convert the rebound.
OptaJoe noted how poor Liverpool's record is from the spot in the Premier League:
James Pearce at the Liverpool Echo neatly summed up Liverpool's first-half performance:
The Reds, however, took just five minutes of the second half to break the deadlock. Sturridge latched on to a poor header from Smith before guiding a clinical finish past Lossl. It was a landmark goal for the Liverpool striker, as shown by Squawka Football:
Sturridge then missed a great chance to double Liverpool's lead after being played through on goal by Firmino, only to see his effort blocked by a sliding Mathias Jorgensen.
Minutes later, Liverpool scored again, with Firmino powerfully heading home Milner's corner to put the hosts firmly in control.
There were further chances too, as Lossl tipped a Salah shot on to the post before Joel Matip headed narrowly wide.
Wijnaldum was not to be denied, though, taking a touch before firing into the top corner to complete the win in some style.
The victory was much-needed for Liverpool after their demoralising defeat to Tottenham, as the Reds roused themselves after a testing opening 45 minutes.