The pair could not be separated after 72 holes in Hawaii, the Japanese and American finishing four shots clear of the rest of the field on 23-under-par.
Matsuyama had enjoyed the marginally better final round, posting a 63 to Henley's 65, but it was his approach shot at the first playoff hole which ultimately made the difference.
From 277 yards away on a par five and with the sun in his eyes, Matsuyama hit a wood off the fairway to leave his shot three feet away, duly converting the opportunity for eagle to end Henley's challenge in the process.
Ireland's Seamus Power and American Kevin Kisner shared third position, while Scotland's Russell Knox started the year with a much-needed tie for seventh spot as he bids to move back up the world rankings.
Englishman and former world number one Luke Donald ended a consistent tournament with a share of 27th place. body check tags ::