After losing to the bottom club Chippenham last weekend, it was a welcome victory for the Bridgers, who have moved up to eighth in the table, with a game in hand on many of their league rivals.
Ivybridge got off to a good start with a try by prop Reece Adams from a catch-and-drive move following a penalty.
The visitors, with the elements in their favour, continued to dominant and Adams scored a second try on 30 minutes to make it 10-0.
However, just before the break Old Centralians scored a drive try, which was converted, to leave them just three points behind.
Matt Grieveson, who had missed two first half conversion, then failed with a penalty almost in front of the posts before replacement Billy Pinkus put one over from almost the same spot. That made it 13-7.
But Old Centralians gave Ivybridge a fright with a second try, but fortunately they could not convert.
“It became a dog-fight, but the players showed real character after last week’s lost,” said team manager Neil Thomson. “We definitely deserved to win. If we had kicked our penalties and conversions we could have won by 10 or 12 points.
“But we got the win and we’ll now look forward to the Barnstaple game at home on the second of January.”
There was no joy in Western Counties West for either Devonport Services or Saltash, who both now find themselves in the bottom three.
Services could move up if they are awarded the four points for last week’s 19-13 win over promotion-chasing Kingsbridge. That game had to be abandoned a few minutes early due to an injury to the referee and Services are still waiting to hear if the result will stand.
They certainly need those points after going down 27-14 at Cullompton, who had started the day on the same amount of points.
Matt Morrison and Luke Stannard scored Services’ tries, with Matt Anstis converting both.
Saltash are just one point ahead of Services in the table after they went down 10-0 away at Tiverton.
That was the Ashes’ sixth straight loss.
Ellery Jones continued his good try scoring form with two more for Argaum. Mason Edwards and Dan James adding their other tries.
After back-to-back wins, Argaum are now just five points off fourth place.
Fifth-placed Plymstock Albion Oaks suffered a disappointing 45-7 at high-flying Bude – a match that was abandoned early after an injury to visiting forward Dan Jones, which held the game up for nearly an hour.
Tavistock are only staying out of the relegation zone on points difference. They lost 15-12 at home to fellow strugglers Hayle, who leapfrogged above them.
In Devon One, there was a vital 21-17 away win for OPMs at South Molton, which was a massive boost for them going into the new year.
OPMs had been struggling to get a side out for the fixture but they showed spirit to return with a valuable four points that moves them above Totnes and New Cross into sixth.
Promotion hopefuls Tamar Saracens’ home match with New Cross was postponed.
However, St Columba and Torpoint did Sarries a favour by denying second-placed North Tawton a bonus point.
Saints produced their best display of the season to narrowly lose 14-5. In the end, Saints were disappointed not to pick up their first point of the campaign.