Morales' single to right in the fifth inning capped a four-run go-ahead rally, plating Alex Santana and Bladimir Franco for a two-run lead. Trailing by two, the Dodgers managed to tie the game earlier in the frame when Jesus Valdez hit an RBI single and scored on an error by Giants catcher Eric Sim.
Houston native Jason West worked out of trouble in the ninth, striking out two after beaning a pair of batters to seal the win with his second save of the postseason.
Unlike most other leagues in the Minors, the AZL hosts a one-game championship each year following a one-game semifinal round. The Brewers claimed the title in 2010.
It's the Dodgers' first Arizona League championship since 1990 and the fifth overall in the affiliate's history. The club is Los Angeles' Rookie-level squad and plays at Camelback Ranch, the Dodgers' new Spring Training facility in Phoenix.
Pitching was the story for the Dodgers on Wednesday -- Noriega came up clutch in relief, holding the Giants to a pair of hits to earn the win. He struck out four after Dodgers starter Jose Dominguez lasted 2 2/3 innings. Dominguez allowed two runs on a pair of hits and two walks.
Steve Matre pitched a scoreless eighth, working around a hit and a walk.
The Giants took an early lead when Eldred Barnett doubled home Sim with two outs in the second. Cristian Paulino hit a leadoff double in the third and scored on a fielder's choice grounder from Kelby Tomlinson.
The San Francisco affiliate's offense stalled thereafter, though -- the Giants' best rally came without a hit in the ninth, when West hit Sim and Elliott Blair to begin the inning. West got Michael Mergenthaler to pop up and struck out Eldred Barnett and Myles Schroder to end the frame and seal the crown.
Right-hander Joan Gregorio started for the Giants and allowed all four runs -- two earned -- on six hits over 4 1/3 innings. He struck out five.
The Giants joined the AZL in 2005 and won a division title last year.