Championship (second tier) side Rotherham, who haven't made it through to the fourth round of the competition since 2001-02, kept their composure early on as Fulham controlled the play.
The race for Premier League places in next season's Europa League warmed up on Sunday when Aston Villa and Everton fought out a thrilling 3-3 draw and Fulham came from behind to win 3-1 at Manchester City.
Manchester City's fingertip hold on their Premier League title was further loosened when a 2-0 loss at Everton followed by runaway leaders Manchester United's 1-0 win over Reading left them praying for a football miracle.
Gerrard's side turned their fortunes around at the expense of the visitors under Lampard
Manchester City went top of the Premier League, at least until Manchester United play at Stoke City later on Saturday, when they beat Everton 2-0 at the Etihad Stadium with goals from second-half substitutes Mario Balotelli and James Milner.
New Everton boss Sean Dyche's reign began with a shock 1-0 victory over English Premier League leaders Arsenal.
Manchester City's Argentina striker Carlos Tevez scored a hat-trick two days after he was arrested as they cruised past Barnsley 5-0 to join history makers Wigan Athletic in the FA Cup semi-finals on Saturday.
Everton can take a huge step towards an unlikely top-four finish and Champions League soccer next season if they can maintain their recent run of great form by winning at Arsenal for the first time in 17 years on Tuesday.
Frank Lampard underlined his value to Chelsea with a well-taken double that secured a 2-1 comeback win at Everton on Sunday to move the Londoners back up to third place in the Premier League.
Everton ended third-tier Oldham Athletic's giantkilling FA Cup run with a 3-1 victory in their fifth round replay on Tuesday to tee up an all Premier League quarter-final against Wigan Athletic.
The battle for Champions League qualification continues with fourth-placed Aston Villa away to Luton Town on Saturday and Tottenham Hotspur, who are five points behind with a game in hand, hosting Crystal Palace.
A summary of sports events and sports persons, who made news on Thursday.
On-loan Bolton Wanderers striker Daniel Sturridge scored his third goal in three games to wrap up a 2-0 victory over Everton in the Premier League on Sunday.
Chelsea came from behind to beat Crystal Palace 3-1 thanks to added time goals from Conor Gallagher and Enzo Fernandez.
Striker Wayne Rooney was included in Manchester United's squad to play at Everton on Saturday after more than a month out with a broken bone in his foot.
Tottenham Hotspur scored three late goals to beat Bolton Wanderers on Tuesday and set up an FA Cup semi-final against Chelsea, after replaying the game that was abandoned when midfielder Fabrice Muamba suffered a cardiac arrest on the pitch.
Everton get the chance to put a large dent in Manchester United's title hopes when they face the Premier League's injury-hit leaders at Goodison Park on Saturday.
Liverpool kicked off the new year three points clear atop the English Premier League standings with a 4-2 victory over Newcastle United.
Manchester United wasted a glorious chance to catch Chelsea at the top of the Premier League when they lost 1-0 at home to Aston Villa on Saturday. Earlier leaders Chelsea were held 3-3 at home by Everton despite two goals from Didier Drogba.
Liverpool moved back to the top of the Premier League with a 2-0 victory at struggling Burnley
Manchester United were humbled 3-0 at home by Newcastle United in the League Cup fourth round
IMAGES from the English Premier League matches played on Saturday.
"In this period, everyone's thinking of New Year's Eve, the distraction can be a problem. Two days after Leeds, we have to be ready."
IMAGES from the Premier League matches played on Saturday.
A summary of Saturday's matches in the English Premier League.
Images from Saturday's action in the Premier League.
Steven Gerrard scored two penalties as Liverpool went back to the top of the Premier League with a 2-1 win at West Ham United to complete a Merseyside win-double over London clubs on Sunday.
The England striker's transfer value soared to 50 million pounds following his Euro 2004 performances.
IMAGES from the English Premier League matches played on Saturday.
Champions Manchester City slipped to a shock first Premier League defeat of the season at Wolverhampton Wanderers on Saturday, while Manchester United's campaign of woe continued with a loss to Crystal Palace.
A ninth successive win in all competitions for United was celebrated with real vigour, as they moved to within a point of City in second, giving Arsenal the chance to go eight points clear at the top of the standings with a win over Tottenham Hotspur on Sunday.
Chelsea beat Newcastle United 2-0 for a 10th successive Premier League home win at their Stamford Bridge stronghold on Saturday to reassert themselves as Premier League leaders while champions Manchester City drew at Everton.
Everton scored twice in stoppage time to snatch an unlikely 3-3 home Premier League draw with Manchester United on Saturday in a game that Wayne Rooney missed to spare him from potential crowd abuse.
Images from Saturday's action in the Premier League.
Manchester City roared back to the top of the Premier League with a 6-1 thrashing of Bournemouth after Manchester United steadied the ship
Tottenham Hotspur continued their Premier League title push with a 2-0 win over Everton on Wednesday to put them level on points with second-placed champions Manchester United and three behind leaders Manchester City.
Video footage appeared to show Ronaldo angrily slapping the phone out of the boy's hand as he walked down the tunnel.
Images from Saturday's action in the English Premier League.
FA bans Ronaldo for two games for smashing fan's phone in April
Manchester City went top of the Premier League, at least until Manchester United play at Stoke City later on Saturday, when they beat Everton 2-0 at the Etihad Stadium with goals from second-half substitutes Mario Balotelli and James Milner.