Martin O'Neill's side came from behind to seal a deserved point after Mark Halsey had awarded a controversial penalty to the visitors before the hosts battled back for a draw
Dimitar Berbatov stroked home a controversially-awarded penalty to give the visitors the lead before Sascha Riether's tap-in doubled the advantage for the Cottagers as Martin O'Neill's side laboured at home.
A spot-kick from Gardner halved the deficit and Sessegon completed the comeback, smashing in a fine low effort from 20 yards.
Neither manager made a single change from either of their previous line-ups as Danny Graham and Steven Fletcher were paired up front from the start for the hosts for the first time in a home game.
Sunderland almost took an early lead as Sessegnon forced a corner in the first minute, but John O'Shea headed Seb Larsson's delivery into the side-netting.
After a sustained spell of Black Cats pressure, it was Fulham who took the lead in the 16th minute, albeit in questionable circumstances.
Ashkan Dejagah took a delayed tumble over Craig Gardner's leg, although contact appeared to be extremely minimal, but Mark Halsey pointed to the spot and Berbatov slotted home to Simon Mignolet's left.
With the hosts failing to get into the game, Fulham nearly doubled their lead as Mark Schwarzer's booming kick got Dejagah behind Gardner again, but the Iranian could only lash the ball across Mignolet and wide.
Fulham had a goal soon after thanks to a magnificent counterattack from a Sunderland corner. Dejagah and Bryan Ruiz carried the ball through midfield before Mignolet parried the former's shot straight into the path of Riether, who tapped into an unguarded net.
The hosts were rocked, but responded in the perfect fashion. Gardner rifled a penalty into the top corner after Senderos had clearly tugged Graham's shirt in the box, under a high ball.
Sunderland came out strongly after the break and should have been level after two minutes, but Graham could only hit a tame effort at Schwarzer from eight yards after Fletcher's initial shot had been blocked into his path.
The hosts began to turn the screw, sending numerous balls into the area, and Alfred N'Diaye headed off-target from 12 yards, shortly after hitting an effort from 25 yards just over.
With 20 minutes to go, the hosts finally levelled, mere moments after almost going two goals down again.
Mignolet saved bravely at Berbatov's feet after a delightful scooped pass from Ruiz and the Black Cats went straight up the other end through Adam Johnson. The winger's cross was blocked but ran to Sessegnon, who smashed in from the edge of the box.
The hosts had a penalty appeal turned down after substitute Emmanuel Frimpong threw his hands up to block a long-range shot, and Larsson's drive from distance flew wide as the west London outfit clung on to their point.