Ryan scored twice in the first period and completed his third career hat trick 30 seconds into the third. Ryan later scored his career-best fourth point with an assist on All-Star pick Corey Perry's score during Anaheim's four-goal third period.
Hiller's career-best shutout streak ended at 178 minutes, 34 seconds on Backes' first goal, but the Ducks' Swiss goalie earned his 22nd victory, matching Detroit's
After Perry put a wraparound into an open net with 13:43 to play, the third period degenerated into a prolonged brawl that included six combined goals, 70 penalty minutes, four fights and two misconduct penalties.
Ryan is embracing a major role for the Ducks in captain
Ryan clinched his third straight 20-goal season with a pair of nifty scores in the opening minutes while Anaheim went ahead 3-0. St. Louis dominated the second period while pulling within one goal, but the Ducks poured it on with four consecutive goals in the third.
Anaheim scored during a power play just 3 1/2 minutes in when Ryan took a cross-ice pass from Lupul and beat Conklin with a short wrist shot before Blues defenseman
Ryan connected again late in the first period after an exceptional pass from Perry, who fought off two defenders while skating behind the net before finding Ryan in front as he fell to the ice.
Ryan deflected home