The South Hams side are now set to meet South West One East outfit Towcestrians in a play-off for promotion to National Division Three South West.
Towcestrians did beat Danny Thomas’ Chippenham 10-8 on Saturday but they are five points behind the former Plymouth Albion captain’s team with one game to go. Chippenham’s points difference is almost 200 better than Towcestrians.
Ivybridge would have secured second place in the west division whether or not they had beaten Cleve, as third-placed Bridgwater where beaten by Camborne.
Ivybridge had led 14-5 at half-time thanks to two tries by George Wilson, but Cleve hit back after the interval to go 15-14 in front before the home side produced a strong finish with a try by Max Sowden and two penalties by Matt Grieveson.
In Western Counties West, Tavistock were relegated after they were beaten 27-3 away at third-placed Tiverton.
Devonport Services also lost away, going down 34-11 to Wadebridge. Matt Anstis scored all the visitors’ points.
That ended Services’ hopes of a top five spot, but they should finish sixth with a home match against bottom side St Ives to come next weekend in their final fixture.
The only team that could overtake them is Gareth Evans’ Okehampton side, who are two points behind.
Saltash will take a one-point lead into the final weekend of the Cornwall/Devon League campaign after they crushed Bude 68-17 at home and their title rivals Crediton missed out on a bonus point away at Pirates Amateurs.
Crediton were losing but came back to win 26-19 to set-up a winner-takes-all show down in east Devon next week.
The pair are more than 20 points ahead of third-placed Withycombe and so both will be playing in Western Counties West next season.
Former Plymouth Albion full-back Max Venables scored four tries and kicked nine conversions for a stunning-38 point haul for Saltash on Saturday.
Elsewhere, already relegated OPMs and Liskeard-Looe both suffered home losses.
OPMs went down 38-21 to Falmouth, while Liskeard lost 21-20 to Hayle at Lux Park.