Zimbabwe international Zhuwao smashed 101 off just 60 balls and Parvess hit 95 at a run a ball as Eversley chased down 253 in 47 overs.
Both were dropped while in the 60s and Wokingham skipper Ryan Pogson admitted those mistakes proved costly.
"I thought 253 was going to be enough, if you played it 100 times I am not sure you would get that result too often, but we paid for the drops. They probably cost us around 90 runs," he said.
"Our bowlers didn't necessarily stick to the plans all the time but they hit the ball very hard and well. The pleasing thing is we kept fighting until the end, we took three late wickets to make sure we got the maximum of 13 points. You never know when those points might come in handy."
After winning the toss and electing to bat, Wokingham got off to a solid start as Stuart Parsons (88) and Previn Shaw (15) put on 43 for the first wicket.
Scott Dyer (1-46) broke the stand when he had Shaw caught by Alex Davidson but Parsons and Chris Nicholas (55) enjoyed an even better partnership than the openers.
They took Wokingham to 178-2 before Sam Glaze (4-32) had Nicholas caught behind by Davidson.
Stuart Hayter was bowled by Glaze the next ball and both Parsons and Simon Myles (7) also fell to the paceman to leave the hosts 196-5.
But a late onslaught from Stevie Smidt (36) and Craig Beales (31), both of whom scored at more than a run a ball, enabled Wokingham to declare on 253-5 from 46 overs.
That looked as though it would be an imposing total as openers Phil Wise (12) and Dyer (13) fell cheaply to Smidt (1-70) and Hunter Greyling (2-23).
However, that brought Zhuwao and Parvess together and they proceeded to smash the bowling around the ground.
Even when Zhuwao, who hit eight sixes, was bowled by Pogson (1-44) just after reaching his century, Parvess continued to score at a fast pace.
He was eventually caught by Pogson off the bowling of Greyling with the score
Ben Saville (22) and Davidson followed soon afterwards, both dismissed by Will Ellison (2-18), but Shane Green and Chris Last saw the visitors home.
Wokingham will be looking to bounce back when they go to High Wycombe 2nds on Saturday while Eversley entertain Beaconsfield (both 1pm starts).
Pogson is set to captain Wokingham for the rest of the season as former skipper Dan Reddyhough has been ruled out of playing for the 1sts due to a hip injury.