Antrim's Allen had been in excellent form since the turn of the year, and won his second ranking title at the Haikou World Open, but was unable to replicate that on the biggest stage as he fell at the first hurdle in Sheffield for the second consecutive year.
Romford's King, a veteran of 14 appearances at the Crucible, will have the chance to reach the quarter-finals for the first time when he takes on Ding Junhui or Alan McManus.
Allen trailed 5-4 overnight but appeared to have the momentum when he won the first three frames tonight to lead 7-5. The next two were shared, then King produced his best snooker of the match at the business end. Breaks of 74 and 89 got him back to 8-8, and when Allen missed a red to a top corner in frame 17, the Englishman capitalised with 81 to edge ahead.
King missed a pink to a centre pocket at 36-0 in the next, but Allen could only reply with 27 before under-cutting a red to a top corner. Kind added 25 points which proved enough.
"I've said it a million times, on my day I can beat anyone," said 39-year-old King. "In the past I have put myself under pressure, so this time I came here with no expectation and just tried to relax and enjoy it.
"I twitched on the pink in the last frame and thought I was going to throw up. But I held myself together and when I potted match ball I nearly started crying. When he won the 12th frame to go 7-5 up he gave it the fist and that spurred me on."
Allen said: "I didn't perform anywhere near my best. Mark played his best snooker of the match from 8-6 down and I missed two reds which were unforgiveable. He went for his shots and started to get them. It's a shame he didn't do that from the start because it would have been a more open game and better for the spectators. Playing Mark didn't suit my game but I knew what to expect and I didn't handle it well."
