Close-range goals from Matt Jarvis and Ricardo Vaz Te had earned Sam Allardyce's side a two-goal cushion at the break, but Hoops substitute Adel Taarabt gave the hosts hope with a wonderful 25-yard strike.
However, a potential Rangers comeback was stalled when another second-half replacement, Samba Diakite, was sent off for two bookable offences.
Jarvis's first Hammers goal since arriving from Wolverhampton Wanderers in the summer gave them a third-minute advantage.
The Portuguese forward ended his six-year wait for a Premier League goal with a tidy outside-of-the-foot finish from Mark Noble's cross.
The talented Moroccan skipped inside before evading two West Ham challenges and bending a shot into the top corner past a motionless Jaakelainen.
Diakite was also soon into the thick of the action, being cautioned for a challenge on Vaz Te before seeing yellow again for a lunge on Guy Demel.
His dismissal, which came just 20 minutes after he came on, hampered Rangers, who had previously threatened a comeback through Cisse and Esteban Granero, but both were denied by fine Jaaskelainen saves.
The Finn continued to excel in the latter stages as West Ham hung on for their first away win of the season, leaving QPR without a win on the road or at home as the pressure mounts on manager Mark Hughes.