Heavitree's point put them level on points with Exeter Civil Service who lost 1-0 at Alphington, but not one club moved into a different position in the league.
Crediton did close the gap on seventh-placed Vospers, to goal difference, as their victory at Lords Meadow took their unbeaten run to 11 games but they were made to fight hard by a determined Cullompton.
"Our boys had too much Turkey the day before," was the response of Crediton assistant manager Robbie Vaughn.
"The result could have gone either way and I was disappointed with our performance although happy with the three points," he added.
Cullompton boss Ray Pratt (pictured right) was clearly disappointed when he replied: "We had the lions share of the game and still went down by the odd goal."
The all-important strike came 20 minutes from time when Cully were penalised for a foul on Richard Blake giving Scott Brimilcombe the opportunity to send his 25-yard free-kick sailing into the top corner of the visitors' goal.
Alphington go into the New Year sporting a seven match unbeaten run after a narrow and uninspiring 1-0 victory at home to Exeter Civil Service.
This was never going to be a classic as the teams struggled with the heavy pitch and strong wind at The Chronicles.
Practically the only goal-mouth action of any note in the first half, came two minutes before the interval as Jason Warren hooked the ball over Civil 'keeper Dean Willis in a goal-mouth scramble.
The visitors came strong in the early stages of the second half with Alphington coming back in the latter stages of the game.
Heavitree's stalemate with Topsham at Wingfield Park was a dour encounter especially in the first half.
The game finally sprang to life after just 80 seconds of the second half as Sean Carstairs broke clear to dispatch a low drive under Adrian Pullin from the edge of the area.
The visitors were on level terms eight minutes later as Scott Dove's corner was met at the far post by Lee Brown's close range header.