Three points, two injuries, one hero: this was a mixed night for West Ham United that ended in pure joy. When injuries to Carlton Cole and Hérita Ilunga were followed by a freakish equaliser for Aston Villa, the scene seemed set for yet another promising performance to end in another disappointing result.

Instead, Gianfranco Zola’s side dug in when they could have caved in and unearthed a new match-winner in Zavon Hines, the 20-year-old who had gone on for Cole in the first half. He clinched the points in stoppage time. The victory was West Ham’s first in the Premier League since the season’s opening day and lifted them out of the relegation zone, while the leg muscle injuries suffered by Cole and Ilunga are not thought to be serious.

“The team is playing better and it could well be the turning point. We gave a demonstration of our desire, our belief, and that’s what we wanted,” Zola, the West Ham manager, said. “There’s a long way to go and the team is alive and ready to fight.”

This was Hines’s eleventh game of the campaign. The quick forward scored twice on his debut for England Under-21 last month and took his first league goal for West Ham last night with a veteran’s composure, evading the attentions of three defenders and coolly prodding the ball past Brad Friedel from inside the six-yard box.

It was a special moment for the player and for a club still digesting Alan Curbishley’s successful claim for constructive dismissal; a club fretting that the closer they get to January, the more likely it is that players will be sold to lessen the financial pressure. Being compelled to hand more prominent roles to promising youngsters such as Hines may not be so bad.

“He’s already been playing and coming on, he’s played against Liverpool and done brilliantly, he’s played in other games and done very well, so I think he’s not a surprise any more,” Zola said. “He has shown a lot of character, a lot of personality. I would have been very delighted with a finish like that. The boy deserves the spotlight.”

Hines was also involved in the first goal. Looking borderline offside, he ran on to Scott Parker’s through ball and fell under Habib Beye’s challenge. The defender seemed to get the ball, but his tackle from behind was risky. Steve Bennett, the referee, booked Beye and gave a penalty that was thumped high into the net by Mark Noble in first-half stoppage time.

James Collins, who was sold to Villa on transfer deadline day — West Ham have not kept a clean sheet since — was booked for arguing with Bennett at half-time. The official managed to even matters on the dubious penalty front early in the second half by deciding that Manuel da Costa had clambered too forcefully over Collins as the West Ham defender headed the ball clear.

Ashley Young took it and missed, his tame effort saved by the outstanding Green low to his left. But West Ham’s relief was short-lived: their luck was to turn again in the 52nd minute.

Cutting in from the left touchline near the corner of the area, Young curled the ball over Green’s head into the far top corner. Either it was a mis-hit cross or the former Watford winger is the new Zinedine Zidane. “If he did mean that, I’m going to shake his hand because it was a great goal,” Zola said.

After that, West Ham were admirably spirited. Beye was sent off with five minutes left, earning his second yellow card for pulling back Jonathan Spector, a substitute. It was the second soft dismissal for a Villa defender in successive games after Carlos Cuéllar saw red against Everton last Saturday.

Pre-match, Martin O’Neill lamented the decision and called for the ability to appeal yellow cards. Afterwards, he was subdued. “I’m not going to talk about it – pointless exercise. I’m disappointed obviously to lose players in that fashion,” the Villa manager said.

You could understand O’Neill’s gloom. Stiliyan Petrov will be suspended for the game at home to Bolton Wanderers on Saturday after picking up his fifth booking of the season, and Emile Heskey was withdrawn at half-time with a back injury.

West Ham United (4-4-2): R Green — J Faubert, M da Costa, M Upson, H Ilunga (sub: J Spector, 8min) — V Behrami, S Parker, M Noble, J Collison — C Cole (sub: Z Hines, 31), G Franco (sub: L Jiménez, 88). Substitutes not used: P Kurucz, J Tomkins, A Diamanti, J Stanislas. Booked: Parker, Franco.

Aston Villa (4-4-2): B Friedel — H Beye, J Collins, R Dunne, S Warnock — A Young, S Sidwell, S Petrov, E Heskey (sub: N Reo-Coker, 46) — G Agbonlahor, J Carew (sub: L Young, 86). Substitutes not used: B Guzan, M Albrighton, N Delfouneso, F Delph, N Shorey. Booked: Young, Collins, Beye, Petrov. Sent off: Beye.

Referee: S Bennett.