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|Huddersfield Town's Tom Ince (centre) vies with West Ham United's Winston Reid (left) and Cheikhou Kouyate during their English Premier League football match. (Ben STANSALL/AFP)|
Obiang got the opener via an enormous deflection and Bilic then pumped the air in relief as much as delight when Ghanaian star Ayew pounced to add the second as West Ham claimed their first points of the season.
Defeat to Huddersfield would have left the charismatic Croat in real danger of becoming the second managerial casualty of the season, after Frank de Boer was fired by pointless Crystal Palace on Monday.
"We started with three away games (they couldn't play at home until the London Stadium was re-adapted after the World Athletics Championships) and three defeats and this was a must-win game," Bilic told Sky Sports.
"I feel the pressure for a whole year now. It is maybe not logical for me to be under pressure after three games but it is modern football. It is my birthday today and this is a great, great present for me."
For Huddersfield it was their first reverse - and the first goals they had conceded - of what has been an impressive start to life among the elite.
A match big on commitment but poor in quality had seen West Ham, with Andy Carroll back in attack after a thigh injury, go close twice in a first half they dominated.
Mexico striker Javier Hernandez was denied by the crossbar while Jonas Loessl got down to smother the ball on the line from James Collins' header after 22 minutes.
However, the hosts deservedly went ahead 18 minutes from time with a piece of luck that had deserted them in their previous three league games.
Obiang's shot looked to be going wide but took a significant deflection off Mathias Jorgensen and gave Loessl no chance, the goalkeeper desperately trying to make up ground but left flailing at the ball.
There was no luck involved in the second as Ayew, who had been sent on as a substitute, took advantage of a Huddersfield defender failing to clear the ball from a corner and tucked it away.
Huddersfield responded gamely with Tom Ince hitting the crossbar but they never threatened to spoil Bilic's party.