The England skipper had endured a miserable 45 minutes on his last appearance on this ground against Aston Villa 10 days ago but he rarely does not turn up for a cross-city clash.
He duly led from the front and his influence plus Liverpool's superior firepower meant the Toffees never stood a chance.
Gerrard's header opened the scoring in the 21st minute and was followed by Sturridge's two in quick succession with Luis Suarez scoring his 23rd of the season just after half-time.
Suarez and Sturridge now have 36 Premier League goals between them and remain the most crucial factor in Liverpool regaining their place among Europe's elite.
They helped lift some of the gathering gloom over the club's failure to strengthen in the January transfer window with exactly the sort of performance to give a much-needed shot in the arm to their Champions League qualification challenge.
It was not supposed to be like this for Everton as, following the 3-3 draw at Goodison Park in November and with their rivals in the top four by only a point, this was billed as the closest derby for years and the Toffees' best chance of ending their 14-year run without a win at Anfield.
Everton manager Roberto Martinez had taken his team to Old Trafford and won for the first time in 21 years last month but facing the old enemy on their own turf proved a different prospect.
They came with the idea of imposing themselves and Ross Barkley, back 24 days after breaking a toe, blasted wide after just 64 seconds.
Everton dominated the early possession but it was the hosts creating the chances with Jordan Henderson, Sturridge and Suarez, twice, denied by goalkeeper Tim Howard.
The less prolific of the trio - Raheem Sterling - should have put his side ahead when Sturridge's brilliant ball juggle and lobbed pass put him through but finishing is still an area the teenager needs to work on and Howard saved with his legs.
Liverpool's deadly strikeforce only allow you so many chances but the all-important breakthrough came from the captain in the 21st minute.
Suarez whipped in a corner and the England midfielder cleverly lost marker Gareth Barry to power home a near-post header which James McCarthy on the line could not keep out.
Gerrard wheeled away to celebrate with Suarez and that prompted some items to be thrown from the section of visiting fans in the Anfield Road end.
It was to prove a double blow for Everton as Barry's attempts to re-engage with Gerrard at the corner saw him clatter into team-mate Romelu Lukaku, resulting in the striker being carried off on a stretcher.
Phil Jagielka forced Simon Mignolet into a good save and Kevin Mirallas fired wide but the momentum was all with the hosts and Coutinho's diagonal pass sent Sturridge sprinting from the halfway line and his pace took him well clear to clip past Howard.
If that was clinical his second, less than three minutes later, was brilliant as from Kolo Toure's long ball forward he hooked a lob almost over his shoulder to easily beat Howard.
For all the talk of Liverpool's creaking backline - with four first-choice defenders out injured - they coped easily with an Everton attack now missing Lukaku although Toure had to produced a great recovering tackle to force Mirallas wide and Mignolet saved at his near post.
Everton needed a positive start to the second half but, having replaced Steven Pienaar with Leon Osman, blew it five minutes in.
Jagielka's misjudgement on the halfway line gave Suarez the minimal opening he required and the Uruguay international raced 50 yards with both Everton centre-backs trailing in his wake to slot past Howard.
Gerrard generously gave Sturridge the chance to complete his hat-trick when Sterling was brought down by the goalkeeper but the England striker ballooned his penalty into the Kop.
To compound his error his greed in front of goal ignited the anger of Suarez, well-placed for the easiest of chances, but there is no doubt this is a partnership which delivers more often than not.