In their penultimate game of a torrid season, the South American ace's deadly first-half double set the Hammers on the way to a priceless victory that lifted them out of the bottom three and left Bolton's UEFA Cup hopes hanging in the balance ahead of next Sunday's finale against Aston Villa.
During a traumatic week at the Reebok, where Sammy Lee took the helm after Sam Allardyce astonishingly went overboard, it had been an equally eventful seven days down West Ham way as the furious four - Charlton Athletic, Fulham, Sheffield United and Wigan Athletic - collectively threatened legal action over the Premier League's failure to deduct points following its Argie-gate inquiry into the signings of Tevez and Javier Mascherano.
But while all the off-field problems had stolen the headlines, both Euro-chasing Lee and survival seeking Curbishley knew that it was out on the pitch where they needed to concentrate their efforts.
And after the victory that gave them a lifeline at Wigan last weekend, the Hammers were, unsurprisingly, unchanged, while Little Sam made just one switch from Big Sam's side that had so destructively drawn with Chelsea as Kevin Nolan replaced Idan Tal in a stifling five-man midfield.
It was always going to be a tight, tense affair for the East-Enders, whose jitters were not helped by the sight of David Thompson depositing an angled chip onto the roof of Robert Green's net within the opening three minutes, before Nicolas Anelka almost capitalised on a mix-up between James Collins and his keeper.
Yet on ten minutes, that early tension lifted when Abdoulaye Meite paid the price for a careless lunge on Tevez, who dusted himself down and curled the consequent, inch-perfect, 20-yard free-kick over the Wanderers wall and under the right-hand angle of the sprawling Jussi Jaaskelainen.
If news of the Argentinian's opener had infuriated the fuming four, then midway through the first half those anger levels would have risen yet higher, when Tevez crashed Luis Boa Morte's unselfish square pass into the six-yard box, beyond the helplessly exposed Bolton keeper, after Bobby Zamora had carved open the Trotters defence.
And just for good measure, two-goal Tevez - who might even have had a first-half hat-trick - then turned provider on the half-hour mark when his floating cross to the far post was spectacularly volleyed home by Mark Noble to give the hearty Hammers a stunning three-goal interval lead.
Lee's first-ever half-time talk could not have been the easiest but at least his fifth-place side emerged for the restart with more energy and enthusiasm and, as the hour-mark approached, Anelka's awkward, low 20-yarder finally forced Green into his first save of the day.
And midway through the half, the French striker then seized upon a mistake by Noble before inviting Gary Speed to waltz into the Hammers box and cleverly side-foot a low, angled 12-yard shot into the bottom right-hand corner.
Despite still having a two-goal cushion, the Welshman's effort set up a nervy finale for the anxious Hammers who somehow steered themselves to the final whistle - and a daunting trip to Old Trafford next Sunday - without incurring any further damage.