OPMs are now up to fifth in the standings after their third league win of the season.
The match could have gone either way, but OPMs showed good game management in the closing stages to see it out.
Shaun Grundy and Mark Hardy scored tries for the hosts in the first half, with Henry Matthews adding one conversion. After the break captain Billy Garratt added a third try, which was also converted by Matthews.
Totnes’ points came from tries two by James Ruddock and a penalty and conversion from Steve Chapple.
OPMs captain Garratt said: “Totnes are very unpredictable, but luckily we got the win, which we are very happy about.”
The Old Boys were pleased with the way they bounced back after losing 50-22 away at Torrington the week before.
“We are much happier this week,” added Garratt. “We did a lot of work on defence at training on Thursday and we performed really well and did exactly what we had done on the training paddock. That got us the win.”