Bay skipper Scott Leighton inspired a second-half comeback - closing the gap to three points with a penalty then levelling the game with another penalty.
Leighton was also involved in the move the led to second five Moss Doran scoring the try which gave the Bay a deserved lead.
"We were lucky to get the win today but we'll take it," said Coast player-coach Ngarimu Simpkins.
Although Coast winger TK Moeke did not score he was the man who set King up for the match-winning tries
Leighton said he was gutted but proud of the way his side performed and none more so than blindside flanker Sione Ngatu, who was outstanding after receiving a yellow card in the third minute.
East Coast 24 (King 2, Fisihoi, Samupo tries; Semple 2 cons)
Poverty Bay 14 (Doran try; Leighton 3 pens)
HT: 12-6