The National League South side appeared to be on their way out of the competition following a first-half goal from Daggers veteran Jamie Cureton.
As the clock was winding down, King reacted by throwing caution to the wind and attacking their League Two hosts.
Dagenham & Redbridge 1-1 Whitehawk
The Emirates FA Cup
Second Round Proper
2pm, Sunday 6 December 2015
Victoria Road, Dagenham
Winners receive £27,000 from prize fund
And when the game rolled into stoppage time, the pressure continued before defender Jordan Rose climbed in the box to power home a header and make sure the Brighton-based outfit’s name is in the hat for Monday’s third round draw for the first time in their history.
"We deserved it, we just threw everything at them," said King, who joined in with the fans’ celebrations at Victoria Road after the game.
"I put six centre-halves up front and we were relentless, there was nothing more than we deserved.
"We just told him [Rose] to go up and we went to two at the back, this is The FA Cup, this is what it's all about.
"I know Wayne [Dagenham & Redbridge boss Burnett] very well and he just said we deserved that.
"Look at the fans, it's amazing and that's what The FA Cup is about, never say die."
The teams will now meet again after next weekend to decide who will take their place in the third round proper among all of the Premier League and Championship clubs.
"We’ll be ready to go again for the replay," added King, whose side have already knocked out Lincoln City at home in the first round.
"And will they fancy coming to our place? Who knows?"