After 12 rounds, Britain’s Joshua triumphed 118-110, 118-110, 119-109 on the three judges’ scorecards.
Victory extended London 2012 Olympic champion Joshua’s perfect pro record to 21 wins from as many bouts but was the first he’d failed to do so by a knockout.
It also saw International Boxing Federation and World Boxing Association champion Joshua add Parker’s World Boxing Organisation belt to his collection.
This result was Parker’s first defeat in his 25-fight pro career.
Saturday’s contest in front of a 78,000 capacity crowd at the Principality Stadium was the first time two previously undefeated heavyweight champions had met for a world title in Britain.
Joshua’s win should move him closer to a bout against Deontay Wilder, the American who holds the World Boxing Council’s version of the heavyweight title.