Bale's double, which took his Premier League haul to 15 goals and only four behind golden boot pacesetter Robin van Persie, was his third this month for Spurs who are chasing second spot in the table.
Bale scored two superb free kicks to hand the London club a 2-1 first-leg advantage over Olympique Lyon in their Europa League last 32 first leg and he was also twice on target in their last match against Newcastle United.
"I don't know how many goals he's scored now but they're all spectacular," said team mate Gylfi Sigurdsson, who was also on the scoresheet in Monday's victory.
West Ham manager Sam Allardyce, whose team played their part in an enthralling end-to-end encounter, said he had never seen anything like Bale's streak of out-of-the-ordinary goals.
"We've one man to thank for tonight's result and that's Gareth Bale. He's the difference and his wonder goals are continuing," Allardyce told Sky Sports.
"I can't say I've ever seen anyone score so many in such a short time. He's done it twice tonight.
"We played fantastic but we've really been beaten by Bale. As soon as he hit it I went 'oh no', I knew it was going in," he said of the 90th-minute winner.
Allardyce's opposite number Andre Villas-Boas also sung Bale's praises, calling his prize asset "world class" and adding that "players like this assume responsibility at key moments."
The left-footed winger was typically modest in his assessment of another hard-fought victory as his team continue to push for honours.
"It's not about me, it's about the team and we played really well. We obviously wanted to get the three points to keep our Champions League hopes alive," said Bale, who has scored eight of Tottenham's last 10 goals in all competitions.