Gudjohnsen had only scored twice all season and this treble was perfectly executed. Granted his third was via the penalty spot, but the first two were of the highest calibre.
For good measure, Chelsea can rely on livewire winger Damien Duff to thrill the crowd and his did this with an excellent strike to complete the rout.
Former Blue Mark Hughes, now boss of Rovers, sent his charges out on to the pitch with one thing in his mind - defend.
For much of the first half, his team followed his mantra to the letter.
Conceding possession anywhere close to the halfway line, Rovers were content to sit deep, play out time and hope that Chelsea's recent goalscoring drought would continue.
However the tactical acumen of Jose Mourinho came to the fore with a couple of inspired changes to his line-up.
In came Scott Parker for his first start of the season and also Glen Johnson at right-back. Both performed as if they had something desperate to prove and both served their boss well.
But it was Joe Cole, restored to a deep striking role in place of goal-shy Mateja Kezman, that shone through and it was his deft chip from just outside the penalty area on 37 minutes that set up the first of Gudjohnsen's three.
The Icelandic striker, playing well of late, but lacking confidence produced a magical piece of skill to volley home, across goalkeeper Brad Friedel's path to nestle the ball into the far corner of the net from eight yards.
Straight from the restart, the ball fell to Frank Lampard in his own half, wide on the left. The England man looked up, saw Gudjohnsen create space and struck the inch-perfect pass into his path.
Gudjohnsen still had much to do - he chested the ball down and in one quick movement flashed the ball wide past Friedel and into the net.
While the first goal calmed the Chelsea nerves as they failed to capitalise on all their pressure, the second goal, set up a second-half onslaught on the Rovers goal.
Confidence is a wonderful thing and Cole and Gudjohnsen could do no wrong.
Within four minutes of the second half, Cole dinked the ball into Gudjohnsen's path. Blackburn defender Craig Short made a crude lunge at the striker, and although the initial challenge looked outside the box, referee Graham Poll pointed to the spot.
Up stepped Gudjohnsen who smashed the ball high and wide of Friedel's left hand to net his third and decisive goal for the Blues.
Poor Blackburn, who had two feeble shouts for penalties of their own in the first half turned down, were in desperate straits.
It took until the 61st minutes for them to record their first shot on target when midfielder Brett Emerton's weak free-kick found its way through the Chelsea wall, but was easily held by Petr Cech.
With the game won Mourinho signalled his changes.
On came Arjen Robben for his debut for the Blues on 63 minutes.
Tiago and Kezman followed soon after, but the Dutchman shone through as his dazzling wing play lit up a dull Stamford Bridge afternoon.
He could have scored with his second touch after 67 minutes only to see his low drive deflected by Friedel for a corner.
But Rovers could claim some sympathy for the fourth goal.
A Wayne bridge effort was judged to have gone off a Blackburn player for a corner when the TV replay showed nothing of the sort.
The resultant set play saw Duff, playing against his former side, free on the edge of the Blackburn area.
In one move he took the ball to his left side and arrowed home a low, left-foot drive that saw the ball edge into the net by Friedel's left-hand upright.