Davis, who had won 28 of his prior 30 fights by knockout, was taken to the limit by WBA super-featherweight world champ Roach in an action-packed all-American bout at the Barclays Center.
Two judges scored it 114-114 while a third gave it to Davis 115-113 -- but controversy erupted over the referee's failure to call it a knockdown when the champion took a knee in the ninth round.
Davis, who then stuck his head through the ropes to have his face toweled off, said he stopped because oil from his hair got in his eye.
He chided fans for booing when he offered that explanation in the ring after the bout.
"They love you and then they hate you," he said.
Roach, one of the few fighters who has tested Davis, took the fight to the champion, weathering a stream of punishing blows and responding in kind.
"I'm one of the best fighters in the world, man, and it showed tonight," Roach said in the ring.
"He probably wasn't wailing when he said grease got in his eye, but if you voluntarily take a knee and the ref's not counting that's a knockdown.
"If that's a knockdown, I win the fight," he added, calling for a rematch.
"I want to run it back," said Roach, who fell to 25-1 with 2 drawn and 10 knockouts.
On the undercard, Dominican Alberto Puello beat Spain's Sandor Martin by split decision to retain his World Boxing Council super lightweight world title.
After 12 rounds of relentless action, two judges gave it to Puello by scores of 115-113 and 116-112 while the third saw it 113-115 for Martin.
Puello remained unbeaten with 24 victories, 10 by knockout.
Martin fell to 42-3 with 15 knockouts, but he gave Puello all he could handle in the early rounds, landing damaging punches to the body.
Puello began to claw back in the second half of the bout, landing two big lefts in the eighth and dominating in the last two rounds.