The New Zealander had a disastrous start, hitting the canvas in the opening seconds, and Parker showed grit along with his classy combinations to secure victory with tallies of 115-113 and 116-111, with Chisora receiving a score of 115-113.
Charging forward, Chisora unloaded right hands with savage intent in the second, then sent Parker slumping to the ropes with a looping hook in the third.
A looping right hand, the shot that forced the knockdown, prompted Parker to flinch in the fifth before Chisora rattled in punches around the belt line.
But Parker, at last, started to stall Chisora with clean right hands in the sixth round.
A flurry of punches from Parker seemed to briefly stun Chisora in the seventh and they shared a shootout at the end of the eighth, swinging in wild hooks.
With Chisora gasping wearily for air, Parker picked him off with jabs in the ninth, while the Kiwi countered sharply in the 10th.
Watch Chisora v Parker and Taylor v Jonas repeats on Sunday, Sky Sports Box Office, from 9am and 4pm. Book it via your Sky remote or book it online here. Non-Sky TV subscribers can book and watch it here.