The Icelandic striker, pushed up front from his midfield berth, took a Tiago pass in his stride after 87 minutes, strode forward, cut in front of the advancing defenders and slotted home coolly with his right foot past the hapless dive of Edwin van der Sar.
Chelsea boss Jose Mourinho jumped out of his dugout in delight, realising the tough match was won and that his side is almost over the finishing line.
Fulham came to Stamford Bridge with the possibility of being dragged into a relegation dogfight. They did not want to lose - and to their credit could have got something from the game.
Chelsea were forced into a makeshift back four with Germany international Robert Huth, normally a centre-back, forced into the left-back slot. William Gallas was absent due to a bad back.
But it was the Blues who had the early play and after eight minutes could have gone ahead.
Damien Duff drove down the left flank to the by-line and centred for Didier Drogba, but the Ivory Coast international's effort flew over the crossbar.
The champions-elect did take the lead after 17 minutes. Joe Cole collected the ball with his back to goal, just outside the penalty area. He turned and unleashed a right-foot shot in one movement and the ball took a slight deflection off Alain Goma and zipped into the back of the net.
Two minutes later Drogba could have finished off the match but his shot wide when well placed.
Fulham, however, showed dogged resilience and earned an equaliser four minutes before the break. Collins John outpaced Ricardo Carvalho and managed to slot home past Petr Cech from a narrow angle.
With a minute remaining of the half John could have notched another goal, but his right-footed volley from outside the area flew agonisingly just inches the wrong side of Cech's post.
This was not the celebration scenario expected by the home fans and it prompted Chelsea's charismatic manager into making half-time changes.
On came Jiri Jarosik for Huth but more important was the return of Arjen Robben for Cole. The mercurial Dutchman made the difference and his exciting performance lifted Chelsea out of their slumber and onto victory.
The reshuffle by Mourinho also resulted in perhaps the most bizarre sight of the season - at left-back was Duff.
But Mourinho's tactical acumen is well known and this resulted in Fulham having to bring Tomasz Radzinski out of the centre of midfield to deal with the naturally left sided player. Huth was never going to move forward, but Duff was a different proposition.
With seconds Robben set up Gudjohnsen to slot home but the striker was adjudged offside.
But the new tempo had been set and in the 64th minute Chelsea took the lead. Robben's mazy wing play was a beguiling sight. He whipped down the line and nutmegged Moritz Volz before sliding the ball across the penalty area.
Frank Lampard seized his opportunity to move forward into the area and dispatched a powerful low shot into the back of the net, with van der Sar well beaten.
The game was beyond the Cottagers and Gudjohnsen's classy finish three minutes from time resulted in a great outpouring of emotion from the players, the bench and the fans.
The title is now within touching distance.