Kenny Dalglish had seen his side lose three league games in succession - and if the league had started in January they would have been in the relegation zone heading into Tuesday night's game - but Gerrard ensured they would not concede local pride or seventh place to their rivals from across Stanley Park with three goals on his 400th Premier League appearance.
Everton's team selection contributed to their derby demise as manager David Moyes dubiously opted to rest a number of players ahead of the FA Cup quarter-final against Sunderland on Saturday, ensuring the game that marked his 10th anniversary in charge of the club was tinged with disappointment.
However, the fact the visiting XI was a weakened one did not detract from a much-improved performance from Liverpool, who found in their returning captain the ruthless figure in front of goal they have been missing this season, and the talisman required to help lighten the mood of Dalglish and the club following recent league results.
The result takes the Carling Cup winners to within two points of sixth-placed Newcastle, and five points clear of Sunderland and Everton.
While Liverpool opted to bring local lads Gerrard and Jamie Carragher back into the starting XI, Everton - unbeaten in seven - made six changes from the side that defeated Tottenham at the weekend, most notably with goalscorer Nikica Jelavic joining Tim Cahill on the bench as Victor Anichebe and Denis Stracqualursi combined in attack.
It led to the intriguing conclusion that Moyes was resting players ahead of the weekend, rather than throwing them into the intensity of a fixture that has seen 20 red cards in the Premier League era, more than any other, and 11 in the past 14 instalments of one of English football's grandest rivalries.
Dalglish had no reservations over using his more established players and, unsurprisingly, Gerrard in particular appeared to relish the occasion. Within seven minutes the returning captain went close when finding space in the box with a glorious touch from a Luis Suarez pass and firing in a low effort that forced Tim Howard into a sprawling save. The rebound found Jordan Henderson but he was denied by a fantastic challenge from Jack Rodwell.
Though an energetic Everton quickly responded when Leighton Baines negotiated his way past Martin Kelly and Henderson, only to see Steven Pienaar fire over the bar from his cut-back, Liverpool enjoyed the better of a hard-fought first half, with strike partners Suarez and Andy Carroll offering very different yet complementary threats with their technical excellence and physical presence respectively.
But in a season that has seen Liverpool struggle so badly in front of goal - their tally prior to Tuesday night was a measly 30 in 27 games - it was perhaps unsurprising to see them rely not on their strikers but Gerrard to open the scoring.
The home side constructed a lovely flowing move on 34 minutes and although they benefitted from a touch of luck when Suarez's pass deflected off Gerrard and into the path of Kelly, who saw his low effort bounce off Howard and away, the skipper's subsequent finish was sublime as he collected the loose ball from 15 yards out and cleverly floated his shot over a crowd of players and into the net.
Kelly almost reprised his starring role in the opener within minutes when he drove forward from right-back once again and fired just wide, and although Stracqualursi tested Jose Reina with a firm header just before the break, Liverpool were good value for their lead at the break.
Liverpool had a concern over Gerrard as their captain limped off the pitch and into the dressing room but he certainly showed no ill-effects in the second half when adding a second on 51 minutes.
Henderson - who has been the subject of sustained criticism this season following his big-money move from Sunderland last summer - played in Suarez with a glorious pass. The Uruguayan then wriggled away from both Sylvain Distin and Phil Jagielka when cutting in from the right and Gerrard arrived to bash the ball home with a fierce finish from six yards.
Duly enthused, Liverpool offered Everton no respite and Carroll fired narrowly wide following another fine piece of work from Suarez before Kelly was just inches away from sliding the ball home from a Stewart Downing cross to the centre of the box.
Though Rodwell then saw a low effort cleared by Jose Enrique just as it appeared to be sneaking in at the far post, Moyes was clearly unhappy with his side's efforts and made a triple substitution on 62 minutes as Seamus Coleman, Victor Anichebe and Stracqualursi were replaced by Leon Osman, Royston Drenthe and Jelavic.
Everton's changes failed to turn the tide on Merseyside though, and with the game meandering to a conclusion, Liverpool, and Gerrard, secured a third in injury time.
The midfielder led a quick break when bursting through the centre of midfield and played the ball wide for Suarez. The forward had a chance to shoot from a tight angle yet cut back and slipped a pass to his captain, who fired home with relish to complete his excellent evening.