The Warriors were in complete command after racing out to an 18-0 lead inside 32 minutes, and still looked to have the game in the bag when they led 22-6 after Manu Vatuvei's 45th-minute try.
But two tries to Manly halfback Daly Cherry-Evans in the final eight minutes tied up the scores, before co-captain Jamie Lyon kicked the match-winning conversion.
Lyon had missed three earlier conversions and the relief was evident to see when he finally found his range when it mattered most.
But King's injury soured the night somewhat for Manly, who kept their top-four hopes alive with their 11th win of the season.
King walked gingerly from the field in the 16th minute after coming off second best while making a tackle, and was sent to hospital for further assessment.
The exact nature of the injury wasn't immediately clear.
Manly were woeful in the first 39 minutes, but a sensational try to winger Jorge Taufua on the stroke of halftime gave the reigning premiers hope of a revival.
Taufua ran onto a pin-point cross-field kick from Kieran Foran and beat two lunging tackles in a 50m sprint to the line to finally get the Sea Eagles on the board.
The first half produced a series of bruising tackles, with several players set to face nervous waits after delivering high tackles.
Manly centre Steve Matai was one to deliver a high hit, while Warriors substitute Sione Lousi produced a crunching sling tackle.
Vatuvei's 45th-minute try gave the Warriors the momentum early in the second half, but from there it was all Manly as the defending premiers staged a stunning comeback.
Tries to David Williams and Foran got the Sea Eagles back into the contest, before Cherry-Evans left the Warriors stunned with a double at the death.
New Zealand's sixth straight loss to Manly left the Warriors' finals hopes dangling by a thread, with last year's beaten grand finalists two points adrift of eighth spot.
In an added blow, centre Konrad Hurrell was helped off the field after just 15 minutes with what appeared to be a serious ankle injury, although he later returned to the field.
A crowd of 20,095 attended the match in another boost to Perth's bid to win their own NRL side.
But it hardly felt like a home away from home for Manly, who had to contend with a pro-Warriors crowd despite the game being in Australia.