Fellow Londoners Tottenham Hotspur, in contrast, went down 2-1 to Bolton Wanderers at a sad White Hart Lane on the day their former manager Bill Nicholson died aged 85. Everton, continuing their remarkable start to the season, remain third one point behind Chelsea after substitute striker Duncan Ferguson headed his first goal of the season to give them a 3-2 win at Norwich City in an earlier kickoff.
Their city rivals Liverpool extended the only perfect home record in the league to four wins by beating Charlton Athletic 2-0 to climb to fifth, nine points off the pace.
Champions Arsenal go for a record 50th league game unbeaten against sixth-placed Manchester United at Old Trafford on Sunday.
At Stamford Bridge, Gudjohnsen inspired Chelsea to their biggest win under coach Jose Mourinho and helped send former Wales manager Mark Hughes's Rovers, who have conceded 10 goals in three games, to one place from the bottom.
RIGHT SIDE
Gudjohnsen scored twice in two minutes late in the first half with shots from right side of the box after crosses from England midfielders Joe Cole and Frank Lampard.
The Iceland striker, who scored Chelsea's second in their 2-0 win over CSKA Moscow in the Champions League in mid-week, completed his hat-trick six minutes after the interval with a penalty after being brought down by defender Craig Short.
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Mourinho said: "I think (Gudjohnsen) has had maybe better matches and he couldn't score (but) today he scored three goals. I think it's more important to score goals for a striker than to play well a lot."
At Anfield, Liverpool scored two of the best goals of the the season so far in the second half.
Defender John Arne Riise, lurking in the middle outside the box in the 57th minute, met a high clearance first time with a low, left-footed volley through a crowd of players and inside the bottom right-hand corner of keeper Dean Kiely's net.
In the 74th, striker Luis Garcia took a square ball from fellow Spaniard Xabi Alonso outside the box and sent a dipping drive inside the top corner past the diving Kiely.
Liverpool coach Rafael Benitez was pleased with his side who came from behind to win 4-2 at Fulham last weekend but were held 0-0 by Deportivo Coruna in the Champions League on Tuesday.
Aston Villa, scoring with a pin-point free kick from Nolberto Solano and a late second by Lee Hendrie, beat Fulham 2-0 at home for their first win in six league matches.
At White Hart Lane, Spurs equalised through Robbie Keane in the 41st minute after defender Radhi Jaidi's opener for Bolton but substitute Henrik Pedersen struck the 75th-minute winner.
Crystal Palace climbed six places off the bottom with their second league win since promotion, livewire striker Andy Johnson scoring twice in a 3-0 win over West Bromwich Albion.