Remy scored 14 minutes into his maiden appearance following his £8million signing from Marseille, but the Hammers were on top throughout, only to find Julio Cesar in inspired form as he twice denied Marouane Chamakh, who might have had a first-half penalty when Clint Hill wrestled him to the ground.
Chamakh's replacement Carlton Cole also was denied by the Brazilian goalkeeper, but Joe Cole was in the right place to tuck in the rebound after 68 minutes for his first Hammers goal in his second spell at the club.
After QPR captain Hill headed over from a corner in the second minute, Remy's desire to make a swift impression saw him caught offside twice.
Chamakh linked well down the left with Mohamed Diame, who got in behind the visiting defence and cut the ball dangerously across the six-yard box. Matt Jarvis got a touch, but saw Cesar, wearing tights to combat the bitter cold, save. From the resulting corner Winston Reid headed the ball down to Kevin Nolan, who was denied at close range by a smart save from the goalkeeper.
The Hammers were continuing to build the pressure before Remy struck. This time the Frenchman timed his run well to race past Reid and meet Adel Taarabt's pass before finding the bottom corner with a low shot from the edge of the box.
West Ham resumed on the attack but this time tested Cesar. Joe Cole's effort was palmed away before Chamakh had a point-blank header stopped. Ryan Nelsen blocked Diame's follow-up shot in a congested area and Nolan could only head the ball over.
West Ham continued to press forward, with Jarvis' cross met by Chamakh, whose poor header was saved.
It was Chamakh's last act as he was replaced by Carlton Cole, who had a major say in the equaliser. Cesar could only palm the striker's powerful header from Jarvis' cross to the feet of Joe Cole for a simple tap in. It was the former England international's first Hammers goal since January 2003, since a 2-2 draw with Newcastle, also at Upton Park.