The forward's 75th-minute shot was deflected into his own net by Julien Faubert and he had the last word with a 93rd-minute strike.
Adebayor said: "Of course we're back in the title race. We believe we can win the title.
"We had something to prove here and West Ham made it very hard for us.
"But we're happy and pleased. Now we must focus on the derby with Spurs on Wednesday."