The Portuguese centre-back nodded home a 90th-minute leveller in a Premier League game in which he had broken the deadlock after just four minutes.
His defensive partner Jos Hooiveld scored an own goal in Southampton's 6-1 humbling at Arsenal and did so again on the south coast when he directed home a speculative John Arne Riise drive in the second half.
Hooiveld, who came on eight minutes into the clash after Frazer Richardson suffered a thigh injury, then saw Kieran Richardson's close-range strike brush off him on its way in two minutes from time, although the goal was credited to the Fulham man.
However, Fonte saved the Dutchman and his side late on to earn Southampton a fourth point of the campaign.
The hosts began brightly and the returning Morgan Schneiderlin fired a wayward warning shot, before Rickie Lambert headed into the side-netting after connecting with a Danny Fox corner from the right.
Southampton had their second corner by the fourth minute and made their early dominance count.
Adam Lallana floated the set-piece in from the left and Fonte's glanced header at the near post looped over goalkeeper Mark Schwarzer and into the far corner.
Richardson was forced off in the eighth minute for the hosts and his departure forced a defensive reshuffle, with replacement Hooiveld forcing Maya Yoshida out wide.
Fulham began to make headway, with Lambert blocking Aaron Hughes from a corner before the Northern Irishman headed over.
Saints, though, were still looking dangerous and came agonisingly close to doubling their advantage as Jay Rodriguez beat the offside trap and pulled back for Lambert, whose right-footed effort just went wide.
The home side continued to press and Jason Puncheon twice came close from 22nd-minute corners.
Puncheon was denied on the goal-line by Sascha Riether and then, from the following corner, the wide man was adjudged to have fouled Schwarzer prior to prodding home.
Lambert forced Schwarzer into action at his near post after collecting a fine pass from Puncheon, but Fulham stepped up the pressure as half-time approached and home goalkeeper Paulo Gazzaniga was required for the first time in stoppage time when Hughes headed goalwards.
The Cottagers again came close as Hooiveld failed to deal with a hopeful long ball and Hugo Rodallega poked wide under pressure from Gazzaniga.
That momentum continued into the second half but it was still Southampton enjoying the best opportunities, with Lambert volleying over a driven Schneiderlin cross from the right.
Schwarzer spilt a hopeful 25-yard effort from Rodriguez after a great surge forward but Fulham were looking a more dangerous opponent and twice came close in the 60th minute.
Gazzaniga did terrifically to push a close-range Rodallega header away moments after Steve Sidwell bundled the ball onto the post.
Fulham could have also been awarded a penalty after Yoshida appeared to handle in the midst of the action.
Both sides made changes in a bid to change the match but it was an earlier substitute whose impact was felt on the south coast.
Riise drilled a low shot from the left and centre-back Hooiveld could only direct it into his own goal, putting Fulham level in the 69th minute.
The goal had been coming and the Cottagers threatened to go ahead, with substitute Kieran Richardson putting a Riether cross over.
Rodriguez nodded wide for the hosts in stoppage time and Saints paid when Richardson fired home off Hooiveld's leg two minutes from time.
The substitute looked to have earned Fulham three points but he gave away a late free-kick from which Fonte headed home to earn Saints a point.