Jurgen Klopp's side could not add to their advantage in the second half, but they cruised to the victory over the newly-crowned A-League champions just three days after clinching a top-four spot in the Premier League.
In contrast, Sydney started with eight of the team who won the Grand Final earlier this month, albeit without A-League MVP Milos Ninkovic due to family reasons.
The Reds arrived in Sydney just 24 hours before kickoff, but that didn't prevent them from making a quick start to the match and Gerrard almost made a dream return to the first team inside the opening minutes when he raced on to a half-volley just inside the area, only to blaze his effort high over the crossbar.
It didn't take long for Liverpool to open the scoring, though, as Sturridge collected Ben Woodburn's pass inside the area before working space to shoot and rolling a precise finish into the bottom far corner with his weaker right foot.
Sydney broke a plethora of records on their way to the A-League title this season, including the most wins (20), fewest defeats (1), most points (66) and biggest winning margin (17 points), but they were comfortably second best to their Premier League opponents from the first whistle.
Liverpool made it 2-0 in the 18th minute with the pick of the bunch as Firmino picked out Moreno's run with a delightful chipped ball forward before the full-back took a touch and flicked an improvised outside-of-the-foot volley past the keeper.
Sydney were forced to wait until 10 minutes before half time for their first clear chance of the contest when Alex Wilkinson rose highest in the area to meet a corner, only to nod his effort narrowly wide.
Liverpool were quickly back up the other end, though, and tested Danny Vukovic through Firmino moments later before the Brazilian unwittingly added his side's third goal with six minutes of the first half remaining.
Sturridge was the creator on this occasion, once again beating his marker inside the box before playing a low ball into the middle which Wilkinson could only slice against the leg of Firmino when trying to clear, sending it flying into the net.
Harry Wilson and Trent Alexander-Arnold drew saves from Vukovic towards the closing stages of the first half as Liverpool went in search of a fourth, but it was Sydney who came closest to adding to the scoreline before the break when former Everton man Dave Carney struck the crossbar in stoppage time.
Gerrard and Carragher both emerged after the interval, but only in order to be given a reception by the 72,000-strong crowd in Sydney as they were replaced by Steve McManaman and Daniel Agger in the first minute of the second half.
Sydney began to pose more of an attacking threat after the interval with George Blackwood and Rhyan Grant having sights of goal in the early stages of the second half, while Adam Lallana squandered a half-chance with the keeper off his line shortly after the restart too.
The half was mostly played at pedestrian pace due to the raft of changes from both sides, but Vukovic was still the busier of the two goalkeepers and he was called into action to deny Alexander-Arnold, Connor Randall and Woodburn to keep the score at three.
Loris Karius was eventually taken off having had precious little to do, but his replacement Simon Mignolet was quickly called into action to deny Chris Zuvela a consolation goal with 10 minutes remaining.
That sparked an end-to-end period of the match which also saw William Mutch somehow fail to convert from close range with the goal gaping after being picked out by a low cross into the six-yard box.
Woodburn then failed to apply the finishing touch to a fine solo run before Matt Simon stole in behind the Liverpool defence at the other end and forced a good save from Mignolet.
Just as Sydney had in the opening 45 minutes, Liverpool ended the half by striking the woodwork when Alexander-Arnold rattled the crossbar from a tight angle, but the visitors settled for their three-goal win in the end as they finished their campaign in comfortable fashion.