Manuel Pellegrini was unhappy with West Ham's defending but relieved to escape with a point against bogey side Brighton.
The Hammers were staring at a fourth loss in four games with Brighton since they were promoted after goals from Dale Stephens and Shane Duffy, both from corners, put the visitors in charge.
But two goals in two minutes from Marko Arnautovic, set up by substitutes Mark Noble and Michail Antonio, lifted the hoodoo as West Ham snatched a draw.
Hammers boss Pellegrini said: "We know Brighton score most of their goals from set pieces, especially corners, so to concede two goals knowing the characteristic of this team, I was very disappointed.
"I don't remember one chance for Brighton except the two set pieces.
"But fortunately we never gave up and the substitutes changed the face of the game. I'm disappointed about the result but very happy with the spirit of the team. Before the game I didn't want to draw but I think we must be happy."
All the goals came in the space of 12 dramatic second-half minutes, in stark contrast to a listless first half notable only for Andy Carroll's first start for precisely one year.
Carroll had already gone off when Brighton made the breakthrough in the 56th minute. Lukasz Fabianski punched a corner straight to the lurking Stephens who smashed the ball back through a mass of bodies and into the net.
Two minutes later Duffy doubled the lead, pouncing at the far post as West Ham's static defence waved another Pascal Gross corner through.
Pellegrini made the double substitution and the changes had an immediate effect as Arnautovic pulled one back when he latched onto Noble's ball over the top, held off Duffy and expertly finished past David Button.
Moments later Antonio reached the byline, just managing to keep the ball in play, before pulling it back for Arnautovic to smash home off the underside of the crossbar to rescue a point.