It appeared as though City's two goals in three minutes from Chris Whelpdale and Chez Isaac had given the Clarets a firm enough foundation to claim their first victory in three matches, but second half strikes from Matt Bower and Marlon Jackson, sandwiching a Tom Harrison dismissal which led to Scott Fenwick blazing over from twelve yards, ensured the visitors returned to Somerset with a point.
In the troublesome conditions of Storm Hannah, either side struggled to combat swirling winds that dragged the ball from side to side.
Despite the difficult weather, it was the Clarets who dominated the opening stages. Whelpdale squirmed into space and directed a tame effort towards goal which struck the lower echelons of the woodwork. The winger drove forward moments later in another inspirational attacking move, but his effort produced a comfortable save for Luke Purnell.
The visitors provided a rare glimpse of attacking threat when Jackson turned Adrian Cascaval in the centre of the pitch. The tricky forward strode forward fifteen yards before sliding the ball beyond Michael Spillane for Jamie Lucas to run onto, but his forward pass trickled through to Nathan McDonald.
Rhys Murphy, searching for his 24th goal in all competitions, found himself in a good position on two occasions; however the City top-scorer could not muster any power as he failed to test Purnell from close range.
City continued to dominate and Fenwick came close to scoring when the Seagulls failed to gain any distance with a poor clearance, but the Geordie striker stabbed a volley wide.
But the deadlock was eventually broken on the half-hour mark when Whelpdale lashed home from the edge-of-the-box. Murphy controlled well 18-yards from goal before skidding the ball to Whelpdale whom, from a wide position, accurately shot beyond Purnell to score his tenth goal of the season.
Having stuggled to score in thirty minutes of play, the Clarets doubled their advantage two minutes after Whelpdale's opener. A long ball was passed inside to Isaac who took one touch to move into space before running off to celebrate his first goal for Chelmsford City as his drilled effort nestled in the bottom corner to give the hosts a healthy first half advantage.
With the wind in their sails, the visitors' late barrage of pressure in the first half continued in the early stages of the second half and culminated in an early goal. City failed to clear their lines from a left-sided and Bower made no mistake at the far post by heading firmly beyond McDonald after being found umarked.
Chelmsford could have extended their lead when a well-practiced corner routine let the ball travel from Isaac to Murphy, but Wraight ended the chance by delivering a shot which skidded into Purnell's palms.
The hosts were handed a glorious chance to restore their two-goal cushion after Harrison was dismissed for dragging Fenwick down inside the penalty area, but the striker was unable to keep his spot-kick down as he blazed over from the twelve yards.
Despite the adversity of relegation facing them directly, the Seagulls refused to be tamed by the fighting-for-promotion Clarets and their hard-work paid evident as they drew level with twenty minutes remaining. A swift counter attack allowed Jackson to cut inside and the 28-year-old executed a sublime curling shot into the top left corner.
Murphy's driving run caused havoc in the Weston box in the last ten minutes, but Purnell stood firm to turn the striker's effort away for a corner.
Weston-super-Mare were millimetres away from a dramatic winning goal when a far-post header crashed against the post before bouncing along the line and out for a goal-kick; City then had a late chance of their own to steal all three points but substitute Aaron Cosgrave's effort was cleared off the line after Purnell was beaten as both sides settled for a point.