The Chiefs took a 24-14 lead at halftime, with Anscombe scoring his first try in the opening minute and inside center Bundee Aki making it 10-0 in the 10th.
Scott Higginbotham put the Rebels on the board with a try five minutes later, but Anscombe scored two tries in seven minutes.
The Rebels were kept in the game by Hugh Pyle, who scored the first of a brace of tries shortly before halftime, but the Chiefs went 31-14 ahead 12 minutes after the break with a try by Sam Cane.
Beale came off the bench early in the second half, making his return from a six-week exile after he was stood down for punching two teammates on the team bus.
Beale helped set up scrumhalf Nick Phipps for a 68th minute try in the left corner with a brilliant break at midfield.
Brodie Retallick pushed the Chiefs’ lead out to 39-26 by scoring a try with 10 minutes left.
That set up a grandstand finish as Beale tore through the Chiefs defense to score a brilliant individual try in the 75th minute.