Albion soared to third in the Premier League as a richly deserved win at the Stadium of Light ensured their best top top-flight start since 1953.
A Zoltan Gera screamer set them on course for victory and helped them complete four straight top-flight wins for the first time since 1980.
A howler from Sunderland keeper Simon Mignolet helped Shane Long make it 2-0 before half-time and substitute Romelu Lukaku added a third from the penalty spot after Graig Gardner had netted for the hosts with a deflected free-kick.
Stephane Sessegnon made it 3-2 late on but Fortune netted a fourth for Albion deep into stoppage time to ensure they went third for at least 24 hours.
The sides traded early chances with Adam Johnson firing straight at Albion keeper Boaz Myhill and Peter Odemwingie’s shot deflecting to Simon Mignolet in the Sunderland goal.
Myhill had to make a much better save on 18 minutes to keep out a half-volley by Stephane Sessegnon after Adam Johnson had flicked on Danny Rose’s through-ball.
The day’s first contentious issue came on 21 minutes when Baggies striker Shane Long was controversially booked for diving under a challenge by John O’Shea.
Replays showed an apparent foul by the defender as Long headed for goal and an Albion free-kick might have brought a red card for O’Shea, who had already been booked.
There was a scare for the Baggies when Sessegnon connected with a Johnson free-kick and Myhill could only parry the shot back into the goalmouth but Gareth McAuley, back after injury, was on hand to clear for a corner.
Albion went ahead on the hour mark as Gera produced a moment of magic.
Odemwingie robbed Johnson and squared for the Hungarian, who fired a curling left-footed shot from 25 yards into the top corner off Mignolet’s fingers.
Two minutes later O’Shea bent a shot just wide after the Baggies could only half-clear a corner.
But the visitors were two up a minute before half-time thanks to Mignolet’s error.
The Belgian slid out to gather Chris Brunt’s over-hit through-ball but fumbled at the feet of Long, who had time to adjust his feet before firing into an empty net.
Sunderland could have reduced the deficit just before the break but Myhill produced a smart save to keep out a free-kick from Gardner, who had replaced injured captain Lee Cattermole.
Myhill was involves again early in the second half with an unconvincing but successful save to keep out a long-range Johnson effort.
And twice Albion could have sewn up the win, first when Brunt’s cross-shot just eluded Long and then when Odemwingie fired the ball across the face of goal, inches away from Brunt.
But the Black Cats reduced the arrears with 16 minutes remaining to set up the potential for a tense finish.
Gardner’s free-kick deflected off Fortune in the Albion wall and looped over a helpless Myhill.
But Albion removed any nerves on 81 minutes when Liam Ridgewell was chopped down in the box by Johnson and Lukaku stepped up to blast the resultant penalty low to Mignolet’s left and into the bottom corner.
Lukaku almost made it 4-1 when he rounded Mignolet and rolled a cross-shot just wide.
Sunderland pulled another goal back when Myhill saved a header from Steven Fletcher, only for Sessegnon to force home the rebound.
But, with the hosts, pushing hard for an equaliser, Albion broke to grab their fourth as Lukaku squared for Fortune, who bent home a superb shot.
By Steve Madeley