Hatherleigh stay hard on the heels of A Division leaders Budleigh Salterton after grinding out a one-wicket win over Plympton.
Justin Wubbeling marked the end of two-match playing ban with a top score of 92 in Plympton's 228 for eight.
Gareth Tidball (2-41) was the only Hatherleigh bowler to take more than one wicket. Charlie Neilson (1-19) was the hardest to get away.
Hatherleigh got a 79-run start through Ryan Dennis (32) and Tidball (23), but they were just the warm-up men for Zimbabwean Tino Mutombodzi.
Mutombodzi thrashed 75 off 61 balls - 12 fours, one six - and with help from Tidball and Rob Cockwill (13) raced the score along to 169 for four with 20 overs to go.
It looked routine from there but Privett (3-53) struck twice and a couple of run-outs showed Hatherleigh were feeling the strain.
Nielson (23) shored up one end, leaving Jasper Preswell (10) and Rueben Forrester to shepherd Hatherleigh over the line with 13 balls to spare.
Hatherleigh's stand-in captain Rob Cockwill, deputising for the holidaying Mark Lake, felt it could have been wrapped up sooner.
"We made hard work of it," said Cockwill.
"We didn't field at well as we can and dropped important catches which would have made the chase a lot easier.
"After a fantastic start to the chase with Ryan Dennis coming in at the top of the order and batting well, we had a slight wobble in the middle with some disappointing dismissals with two run outs.
"To be fair Plympton bowled very well after a poor start and clawed it back.
"At the end of the day we didn't play that well and still managed to win. So we just move on to next week."
Hatherleigh are at home to promotion rivals Bradninch this Saturday.