Derbyshire 321 and 269 for 6 (Godleman 86, Haider 65, du Plooy 52*) lead Worcestershire 473 (Waite 109*, D'Oliveira 89, Chappell 5-69) by 117 runs
The former Yorkshire all-rounder passed his previous highest first-class score of 59 to end unbeaten on 109 from 149 balls which took Worcestershire to 473, a lead of 152.
Worcestershire's prospects of such a sizeable lead appeared slim when Brett D'Oliveira was run out in the second over of the day.
He had added only two to his overnight 87 after he came back for a third run and was stranded when Brooke Guest relayed Anuj Dal's throw to the bowler's end leaving the Worcestershire skipper stranded.
D'Oliveira departed kicking the air in anger but if Waite thought he was to blame, he more than made up for it with the best innings of his career.
With the help of the lower order and some generous assistance from Derbyshire who persisted with short-pitched tactics for too long, Waite transformed a decent advantage into a potentially decisive one.
Both Joe Leach and Josh Tongue were caught at leg gully by Wayne Madsen, one of them a blinder, but from then on Derbyshire's morning went pear-shaped.
Gibbon lobbed a bouncer from Suranga Lakmal to short midwicket but it was signalled a no ball and that cost 75 runs.
Waite pulled Ben Aitchison for two consecutive fours to take the lead into three figures before he cut the left-arm spin of du Plooy for his 14th four to bring up his century from 143 balls.
The fact that all the Derbyshire players applauded showed just how well Waite had played from the moment he came in with his team still in arrears.
Gibbon was by no means a sleeping partner, pulling Matt Lamb's leg spin for six and driving him through the covers for another boundary before Chappell finally put an end to Derbyshire's frustration.
A chipped catch to midwicket gave Chappell his fifth wicket, making him the 14th Derbyshire player to take five in an innings on debut, although few in the home dressing room would have been in the mood to celebrate.
It was now a case of how Derbyshire would respond after such a chastening passage of play and they came out as if determined to wipe out the deficit before tea.
This was Billyball take two as Godleman and Haider went after Worcestershire from the off, unsettling the bowlers who could not find a consistent line or length.
Godleman was first to his second 50 of the match which came off 55 balls and Haider reeled off some glorious off-side strokes as the pair sailed along at more than five an over.
Haider pulled Waite for six and drove him down the ground for three to reach his first 50 for Derbyshire but two wickets in the last two overs of the session lifted Worcestershire.
Haider was lbw as he pushed forward at D'Oliveira and Brooke Guest was bowled when Leach straightened one to take the off stump.
Godleman and Madsen put Derbyshire in profit but Leach pinned Madsen with a full length ball before Gibbon brought one back to bowl Godleman.
D'Oliveira beat Lamb's forward push and Dal was lbw to Waite leaving du Plooy as Derbyshire's best hope of setting a challenging target.