Striker Jordan Young's second-half double ensured it was the Bluebirds who leapfrogged the Hawks into seventh position to claim the last remaining play-off place.
In front of a bumper Westleigh Park crowd of 2,290, Hawks required at least a draw against Chippenham but Young's strikes on 69 and 77 minutes made sure it was the Wiltshire side who instead would be heading for the lottery of the play-offs.
In honesty, other than an early Manny Duku header which he sent wide and an appeal for a penalty after Jake McCarthy went to ground seconds before Young’s second, Hawks lacked fluency and struggled to create too many openings on such a big final-day occasion as they were summoned to another season in the National League South.
Hawks came flying out the traps with Scott Rendell just unable to get on the end of Manny Duku's header diverted goalwards after just three minutes.
This time it was Duku who sent a stooping header wide at the back post having met Tommy Wright's superb left-foot delivery on six minutes.
Again, the Hawks threatened but to no avail. Jake McCarthy's raking pass sent Josh Passley clear down the right but Spencer Hamilton did brilliantly to beat James Roberts to the cross as he was poised to take a strike.
But the hosts had a huge let-off when Jordan Young did brilliantly to dispossess Ben Stroll, then cut inside to beat Joe Oastler, only to send his attempted curling effort wide of the far post on 23 minutes.
McCarthy started and nearly finished a Hawks move as they continued to search for the all-important breakthrough. The midfielder won the ball back in the centre of park, sprayed wide for Roberts, getting onto the end of his cross but sent a shot wide of goal eight minutes after the restart.
Things were beginning to become tense with Ross Worner spilling across but, fortunately, Joe Newton was able to hack away the loose ball, then Joe Hanks so nearly got on the end of a dangerous cross.
Yet Chippenham would grab the crucial goal required to lift them into the play-off places on 69 minutes. Young took a superb lifted pass in his stride, keeping his composure to slot past the onrushing Worner.
The Bluebirds then bagged a second, through that man again Young, just seconds after they'd had a penalty appeal waved away by referee Dale Wotton as McCarthy went to ground in a crowded Chippenham area from a corner.
A break would follow, with Young sent racing away and he thundered past Worner from a tight angle with 13 minutes of normal time left to play.
There was to be no late rally from Hawks, though, who were unable to extend their season by reaching the play-offs.
Hawks: Worner; Passley, Shroll, Oastler, Newton, McCarthy, Rooney, Duku, Wright, Roberts, Rendell. Subs: Clifford (Rooney, 55), Payne (Rendell, 65), Andrews (Wright 78), Collins, Read.