Thomas, whose late father David had a distinguished career with Beaconsfield and Surrey, has taken over the reins at Wilton Park from Sam Musk.
Thomas led the way as Beaconsfield reached 207-9 from their 45 overs, before becoming the first wicket in a h-hat-trick for the Chesham leg-spinner Andy Goddard.
Jason Harrison made 35, while a late flurry from David Heavyside (21) took the total past 200.
Two players dominated the second half of the match, Mark Eteen, made a classy 91 for Chesham, while the Beaconsfield seamer Jon Mahood, despite having troubles with new footwear, returned the amazing figures of 6-24 in his nine overs.
Beaconsfield looked like winning, when Chesham's last pair required 11 to win from the final three balls, but a leg-side wide that went to the boundary changed the dynamic and edged boundary off the last ball gave them dramatic success.