After a forgettable first half which produced little in front of goal, Nolan struck from close range on 40 minutes amid some contentious scenes and an unsuccessful protest by the Villa players.
Mark Noble threw a free-kick into the Villa box that was headed on by Ciaran Clark. The ball broke to the unmarked Ricardo Vaz Te, who cut the ball across goal for Nolan to apply the finish from close range with Shay Given stranded.
The linesman had his flag up for offside against Vaz Te, but after consulting referee Mike Dean the goal was awarded. Replays confirmed that the decision was correct with Clark rather than home player James Collins connecting with Noble's delivery.
Nolan has now scored five goals against Villa, the most he has managed against any other Premier League side.
Villa looked doomed even at that point as they huffed and puffed their way through the second half without ever looking likely to break down the home side amid some sweltering conditions in London.
In contrast, West Ham United manager Sam Allardyce has now won five of his last seven opening day Premier League matches as a manager.
They could and should have added a second two minutes into injury time when new signing Modibo Maiga - on for the hard-working Carlton Cole - rounded Given only for Nathan Baker to dash back to make the clearance but the three points had already rested with the home side.
Jack Collison missed the match but Collins started against his former club. The 23-year-old Collison played a key part in the Hammers' promotion via the play-offs but aggravated an existing knee injury in the process, which has seen him miss pre-season. Fellow Wales international Collins was fit again after a groin injury, while the home side's other new signing Alou Diarra did not feature.
Villa's Brett Holman shook off a knee problem with central defender Ron Vlaar, right-back Matthew Lowton and midfielder Karim El Ahmadi also starting. Striker Gabriel Agbonlahor (knee), defender Richard Dunne (groin) and winger Marc Albrighton (foot) were all missing for Lambert's first competitive match in charge.
Most of the best moments of the match took effect in the second period after Nolan had drilled a free-kick wide of the visiting goal on 34 minutes. Stephen Ireland knocked a volley into the arms of Jussi Jääskeläinen on 47 minutes, but Villa would not win their first corner of the game until after the hour-mark as if to illustrate their lack of forward momentum.
Cole appealed for a penalty on 50 minutes after tangling with Dutch defender Ron Vlaar - who sported a head bandage after cutting his head earlier - but referee Dean called it right by waving play on.
Vlaar was called into action to clear a couple of yards from his goal on 65 minutes after Vaz Te had played in Nolan while Jääskeläinen made a smart diving block to hold a Vlaar long ranger on 75 minutes.
Cole had a glorious chance to net with a header 13 minutes from time after Matt Taylor threw in a free-kick, but the ball dropped wide.