The winner will host India in April for a place in September's World Group qualifying round, a position New Zealand hasn't been in for the best part of two decades.
Statham battled for nearly two hours before accounting for Wu and Tennis New Zealand High Performance Manager Simon Rea says it was as well as he's seen Statham play.
It's Statham's first win over Wu after losing two five-setters in Davis Cup to him previously.
"Rubin (Statham) played one of the best matches he's played in the last few years to beat Wu. He showed all his experience and desire to earn a valuable point. He has the most wins of any New Zealand player in Davis Cup and it really was an incredible effort," said New Zealand captain Alistair Hunt.
Wu dominated the early exchanges breaking Statham three times in the opening set. But Statham was competitive on his opponent's serve, however he could only convert one of four break point chances.
But Statham got off to a flying start to the second set as Wu's level dropped.
With two early breaks Statham raced to a 4-0 lead before Wu rallied and broke Statham when serving for the set at 5-2. But Statham made no mistake a second time and served it out 6-4 to force a decider.
Some wonderful returning from Statham earned a break in the opening game and he consolidated and then edged ahead. Statham faced two break points serving at 3-2 but held, and then held serve twice more to secure a crucial win for the Kiwis.
Venus stepped on court in the knowledge the pressure was off to some extent and dropped just six points on serve in the first set against Zhang.
In a tight first set, Venus served brilliantly, and broke in the 12th game to take it 7-5 in 39 minutes.
But Zhang was a different player in the second and third sets and romped to the victory in one hour and 49 minutes as Venus struggled to get his first serve in.
