The Blues fiercely battled to hold on to their lead in the second half, having lost both Reece James and Andreas Christensen to injury in the first 45 minutes, but could not see out the victory.
Lukaku headed Chelsea into a 1-0 lead on 27 minutes, turning in a corner in style.
The Belgian hitman shrugged off Neal Maupay's measly challenge, with the Brighton's striker's protests dismissed without issue by the officials.
Chelsea's lead eased their latest initial injury frustration after James hobbled off with a suspected knee problem just moments prior.
The England right-back had deputised at left wing-back in Ben Chilwell's continued absence, but may now face a spell on the sidelines of his own.
At the end of the first half, Chelsea were arguably fortunate to remain with 11 men on the pitch.
Antonio Rudiger flew into a challenge with both feet off the ground, but only saw yellow.
Brighton piled on the pressure in the closing moments, though could not equalise before the break.
At the start of the second half, Christensen did not re-emerge having struggled with injury issues during the first 45 and was replaced by Trevoh Chalobah.
This will cause concern ahead of the important clash with Liverpool on Sunday.
Brighton picked up where they left off as Edouard Mendy stood firm under efforts from Yves Bissouma and Maupay.
The Blues had a penalty appeal from Christian Pulisic waved away, then saw Callum Hudson-Odoi spurn an excellent chance on the breakaway.
It was one of Hudson-Odoi's last actions of the game, as he was replaced by N'Golo Kante with 25 to go.
With Kante on the pitch, Chelsea quickly looked a different team and faced far fewer threats.
However, Welbeck popped up with an exquisite header at the start of stoppage time to snatch a point for the visitors.
The goal and point were both Brighton's first ever at Stamford Bridge.