Lamela struck with a cool header late in the first half at the London Stadium to give Tottenham their fourth successive league victory.
That made it five goals in just eight appearances this season for Lamela, who was making only his second league start of the campaign.
Lamela could start more often after this influential display underlined his improvement since returning from over a year of injury problems that required surgery on both hips.
Thanks to Lamela and a sturdy defensive display, Mauricio Pochettino’s side were able to celebrate five successive top-flight London derby wins for the first time since January 1961.
It was the ideal warm-up for next week’s crucial Champions League trip to PSV Eindhoven and the Premier League clash against champions Manchester City a few days later.
West Ham’s second consecutive loss punctured the optimism sparked by their win over Manchester United earlier in September.
Adding to West Ham’s woes, winger Andriy Yarmolenko was taken to hospital after suffering a serious ankle injury.
Pochettino is adamant Tottenham can cope despite a raft of injuries to key players, including Dele Alli, Danny Rose and Jan Vertonghen.
And even without so many stars, Tottenham were quickly into their stride.
Probing intelligently through Lamela and Lucas Moura, Tottenham worked space for Moussa Sissoko, whose deflected strike flashed just over from the edge of the area.
There is little love lost between West Ham and Tottenham fans, their animosity creating a tense atmosphere in the stands that inevitably led to a bruising encounter on the pitch.
The frenetic tempo claimed a casualty when West Ham defender Pablo Zabaleta needed treatment for a head injury that left blood pouring from a wound above his eye.
– Extra gear –
Harry Kane has endured constant claims that he is suffering from post-World Cup fatigue and the England captain once again looked a little laboured in his movement.
When Moura’s pass sent Kane through on goal, the Tottenham striker couldn’t find the extra gear to accelerate away from the West Ham defence and his shot was scrambled clear.
Given another sight of goal, Kane again reacted too slowly and Issa Diop had time to make the block that kept Tottenham at bay.
Despite Kane’s lethargy, Tottenham were the dominant force and took the lead in the 44th minute.
Sissoko twisted and turned on the right flank before whipping over a cross that Lamela met with a perfectly-timed run, the Argentine heading powerfully past Lukasz Fabianski from close-range.
It took a good save from Fabianski to prevent Davinson Sanchez doubling Tottenham’s lead moments later.
Tottenham keeper Hugo Lloris made an even better stop, leaping to his left to repel a header from Marko Arnautovic early in the second half.
Lloris won another duel with Arnautovic on the hour, this time keeping the striker’s low drive with an out-stretched hand.
Sanchez squandered a chance to kill off West Ham when the defender, picked out by Kieran Trippier’s cross, headed woefully over from close-range.
West Ham pressed hard in the closing stages, but Javier Hernandez’s effort was ruled out for offside and Lloris denied Arnautovic as Pochettino’s men held firm.