Goals from Yarmolenko and Creswell earned West Ham their second successive home win against Manchester United who lost Marcus Rashford through an injury in the second half.
Yarmolenko opened the scoring on the stroke of half time sending a low finish past David de Gea.
Creswell sealed all three points for Hammers in the second half with a superb free-kick into the top right-hand corner.
Chances were at premium in a cagey first half at London Stadium. The Noble’s deflected effort from Pablo Fornals’ free-kick was the closest either team came to a breakthrough before Yarmolenko’s strike.
Juan Mata should have leveled for the visitors two minutes into the second half but failed to hit the target after connecting well with Andreas Pereira’s low cross.
The result lifts West Ham above the Red Devils in the table, while Ole Gunnar Solskjaer’s side remains three points off the top four and without an away win since February.
Nemanja Matic and Rashford were the sole survivors from Thursday’s win, with teenager Mason Greenwood unavailable due to tonsillitis.
Rashford has gone five matches without a goal in open play. Today, the striker looked short on confidence failing to register a single shot before going off injured.
The 21-year-old went down holding his thigh on the hour mark as United suffered a 2-0 defeat.
The injury brought in a deep frustrating afternoon for Solskjaer. His side looked lackluster, lethargic and short of ideas in the final third.
Matic’s long-range drive was easily held by Lukas Fabianski. It was the closest they came to a goal in a forgettable first half.
The visitors improved marginally in the second half. They should have restored parity when Mata got on the end of Pereira’s delivery. However, the veteran midfielder somehow managed to steer the ball wide from point-blank range.
Harry Maguire also went close to bringing the visitors level before West Ham’s second goal, firing straight at Fabianski after the Hammers had failed to clear a corner.
The defeat extends Manchester United’s poor away from their last league victory on their travels which came at Crystal Palace on 27th February.