The Rebels made the trip to Wiltshire off the back of consecutive home wins against Dulwich Hamlet and Hungerford Town.
Meanwhile hosts Chippenham were winless in their seven previous fixtures, although they had drawn five of those contests.
Adam Hinshelwood rotated his squad after back-to-back home wins, bringing Mo Dabre, Davide Rodari and Liam Vincent back into the starting eleven. That meant that Danny Barker, Lewis White and Reece Meekums dropped to the bench.
After a cagey first ten minutes, Worthing’s first attack brought the opening goal. James Beresford crossed into Josh Chambers who was tackled as he hit it, but the ball rolled straight to Dabre who was on hand to net against his former side as he placed it into the bottom right corner.
The Bluebirds were soon back on level terms though as Owen Windsor played in the wide-open Alex Bray on the left side of the box and he confidently fired in at the far post.
Dabre quickly turned from hero to villain after picking up two yellow cards in the space of seven minutes before the half-hour mark. Two similar late challenges forced the referee to reach for his back pocket, sending Dabre for an early shower.
A chance followed five minutes later for Ollie Pearce who dribbled at pace into the area before unleashing a shot which Will Hendry saved. The rebound came quickly at Rodari who couldn’t control it and the ball rolled out for a goal kick.
Pearce cut a frustrated figure during the first half and was denied a penalty after going down under a challenge in the box on 35 minutes.
Ten-man Rebels shut up shop for the final five minutes of the first half, giving up nothing before the interval to set up an intriguing second half.
The Reds came out in a 4-4-1 system as they aimed to limit the number of chances the Bluebirds could create with the extra man advantage. The hosts had plenty of the ball but only managed to create half chances before the hour mark.
Pearce reminded the hosts of the threat that the Rebels posed on the break as he broke away before firing wide from a tight angle on the right.
On 68 minutes, Hinshelwood turned to his bench for fresh legs as he made a triple change replacing Rodari, Vincent and Chambers with White, Meekums and Barker.
The triple substitution certainly gave the Reds a boost with the side able to get further up the pitch with the added pace of Meekums and White.
On 75 minutes the hosts had a penalty appeal turned down after Bray went down under a challenge from Dan Bowry.
The Rebels stood strong and limited the hosts’ chances until added time when Tom Mehew cut back to Windsor who squandered the big chance for the Bluebirds to win it.
A hard-earned point for ten-man Worthing ahead of a tough week on the road which sees the Reds head to Arbour Park to take on Slough Town on Saturday.