England midfielder Frank Lampard opened the scoring with a deflected free-kick midway through the first half before Gudjohnsen extended the advantage six minutes before half-time after some wonderful dribbling skills by Glen Johnson.
Southampton substitute Kevin Phillips ensured an exciting finish by pulling a goal back within six minutes of coming on as a replacement, but Gudjohnsen was on hand to settle any nerves the away supporters had by grabbing his second and Chelsea's third goal seven minutes from the final whistle.
Jose Mourinho's side now lie a massive 13 points clear of their nearest challengers Arsenal and Manchester United at the top of the table and can wrap up their first title since 1955 with three wins in their remaining seven matches.
Mourinho was forced to make one change in his defence recalling Johnson in place of Paulo Ferreira who was sidelined with a foot injury while he also chose to name giant German defender Robert Huth in his starting line-up to try and counter the presence of Southampton striker Peter Crouch.
Crouch came into the match as the Premiership's in-form striker with ten goals in his last 13 games but it was Chelsea who took control of proceedings early on and they opened the scoring in the 22nd minute thanks to the impressive Lampard.
Striker Mateja Kezman was hauled down from behind by Andreas Jakobsson and Lampard stepped up to strike a 35-yard free-kick which took a deflection off the wall giving Saints goalkeeper Antti Niemi no chance.
Kezman twice went close to extending the lead in the next three minutes with half-chances but he fired over the crossbar while Southampton had to be content with trying to hit the Premiership leaders on the break.
But Harry Redknapp's side, unbeaten at home in the league since September, should have equalised in the 32nd minute through defender Claus Lundekvam. Rory Delap's long throw from the right found the Norwegian unmarked just six yards out but the defender could only head wide much to goalkeeper Petr Cech's relief.
Niemi produced two wonder-saves to prevent his side going further behind soon after as he first deflected a back-pass from Lundekvam for a corner at full stretch and then got down smartly to his left to block a well-struck effort from Huth.
But the Finn was powerless to prevent Gudjohnsen from scoring his 13th goal of the season in the 39th minute. Johnson was the creator as he drifted past four challenges before squaring for the striker to clinically finish inside the left-hand upright.
Kezman became the first player to be booked in the 62nd minute when he felled Olivier Bernard and the striker was lucky not to receive a second caution two minutes later when he appeared to elbow Jakobsson.
It was with some relief that he was replaced by Didier Drogba a minute later but the incident seemed to spur Southampton on and they pulled a goal back through Phillips in the 69th minute.
Cech had done well to deny the substitute's close-range header a minute earlier from Crouch's pull-back but he could do little to stop Phillips side-footing home left footed after Paul Telfer had picked him out with a pin-point cross from the byline.
Southampton surged forward with renewed hope of gaining an unlikely equaliser in their quest to boost their relegation survival hopes but Chelsea stepped up a gear and Gudjohnsen was on hand to kill off their hopes of a point in the final seven minutes.
The Icelandic star exchanged a neat one-two with Drogba on the right-hand side of the area before having little trouble in steering a shot across the face of goal and inside the left-hand upright to net his 14th goal of the season and leave Chelsea closer to their Championship dream.
MAN OF THE MATCH: Frank Lampard (Chelsea) – Fresh from his double success with England, the midfielder maintained his impressive form with another masterly display. He opened the scoring and was outstanding in the Blues' engine-room.