But with three tough games remaining, they know that it is still a tall order to finish above Whitehaven.
The Cumbrians hold second spot at the moment, but are just three points in front of Jarrow, who have two games in hand.
While Whitehaven
enjoyed a 3-0 victory at Coxhoe Athletic, Jarrow left it extremely late before winning at Windscale, with a penalty converted by Craig Armstrong in the 90th minute.
Jonathan Matthews had given Bell's side a seventh-minute lead, but Windscale belied their second from bottom position, and hit back with goals from Peter O'Donnell and Ryan Fitzwilliam.
Andrew Willkinson restored parity, and Armstrong kept his nerve in the last seconds to keep the pressure on Whitehaven.
Bell said: "We've just got to try to win each remaining game, but it's going to be difficult. Whoever finishes second will have deserved it."
Jarrow host BOLDON in a local derby on Wednesday night, and Malcolm Reay's side will be hoping to restore a bit of pride after they were thumped 4-1 by Willington on Saturday.
Willington were full value for their victory, as Adam Blenkinsopp converted two penalties, with Peter Mulholland and Andrew Howard also on the mark.
Stephen Green claimed a consolation goal for Boldon.
SIMONSIDE rounded off their Durham Alliance campaign with a 3-1 victory over Shildon Railway, though it needed a second-half comeback to get all three points, after Terry Gillen had given the visitors a 37th-minute lead.
Sean Flood set up Owen Gibson for a 53rd-minute equaliser, and five minutes later Alan Moore stayed on his feet to create a chance for Shaun Edwards.
The win was sealed in the 67th minute when Flood latched on to a long ball from Kevin Tron, and beat two men to score.
Sima boss Gordon Diamond said: "We've had a good season to finish fourth, and we're looking to push on and get some silverware next season."
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