Nash played well without being able to match Finch’s power and while he and Stiaan van Zyl were adding 48 in 29 balls for the second wicket Sussex had a chance.
The 30-year-old equalled the Surrey record of seven sixes in a T20 innings held by Mark Ramprakash, striking four of them in a remarkable assault on David Wiese in the 18th over.
Finch finished on 114 off 64 balls with seven fours and seven sixes, the other three struck during the power-play. Roy cleared the ropes four times in a 33-ball half-century before holing out to deep mid-wicket.
But van Zyl was caught at deep mid-wicket for 29 off Gareth Batty’s first ball and it turned into a profitable afternoon for Surrey’s captain.
Taylor’s side must now beat Essex at Hove on Friday to have any chance of squeezing into the last four while Surrey will probably need to win both their remaining games. Both are among five counties locked on 12 points in the table.