An impotent West Ham display looked set to be punished midway through the second half, when quickfire goals from Dale Stephens and Shane Duffy put Brighton in control.
But Manuel Pellegrini's side responded well and, after scoring his first goal since November 3 to haul the hosts back into the contest, Arnautovic levelled proceedings in the 68th minute.
Michail Antonio and Declan Rice almost completed the turnaround in the closing stages, but Brighton held firm to frustrate their hosts.
Martin Montoya's error gifted West Ham their first chance, but Felipe Anderson snatched at his first-time strike, while Lewis Dunk was perhaps fortunate that his clumsy challenge on Arnautovic did not lead to a penalty prior to the break.
But it was the visitors who struck first – Stephens hammering in on the half-volley after West Ham failed to clear a corner.
West Ham's misery was compounded two minutes later, their set-piece frailties again haunting them when Duffy escaped his marker before expertly turning home.
Duffy was helpless to prevent Arnautovic pulling one back with a neat finish soon after, however, and the comeback was complete two minutes later.
Having left Brighton's defence in his wake, Antonio managed to turn a cut-back into Arnautovic, who prodded in off the bar, with the goal standing despite the visitors' protestations that the ball had gone over the line.
Antonio almost turned the hero late on, only to lash over from close range before Rice hit the side netting as West Ham had to settle for a share of the spoils.
Hammers show their steel
West Ham enjoyed a brilliant December with five wins from seven, although it looked as though they were heading to a second successive defeat until Arnautovic stepped up.
The Hammers are now into the top half, while Brighton – who are unbeaten in three games following a run of three defeats – remain 13th.
Arnautovic bounces back
Having missed much of December through injury, Arnautovic struggled against Burnley last time out, but turned on the style to score his sixth and seventh league goals of the campaign. With him back on form, West Ham will be confident of mounting a challenge for seventh in the second half of the season.
