Marcus Thames had three hits and an RBI for the Yankees, who took two of three from Baltimore to finish a three-city road trip with a 5-4 record.
Burnett (3-0) struck out four and walked one to improve to 10-2 lifetime against the Orioles. He allowed only two runners past first base, and only one reached third.
Burnett has been pitching in the majors since 1999, and this is the first time he's 3-0.
The right-hander received plenty of help from Cano, who got three hits to lift his AL-leading batting average to .407. Cano hit a solo homers in the fourth and eighth innings, his sixth career multihomer game.
Cano has hit in eight straight games and is on a 16 for 24 tear.
The defeat dropped Baltimore's record to 4-18, worst in the majors. The Orioles are 1-8 at home and 3-12 against the AL East.
Matusz (2-1) allowed three runs and nine hits in six innings. The left-hander had won six straight decisions since Aug. 15, including at Yankee Stadium in September.
New York got a first-inning run when Derek Jeter hit a leadoff single, took third on a double by Mark Teixeira and scored on a fly ball by Alex Rodriguez.
Despite collecting his 13th RBI, Rodriguez went 0 for 3 and is hitless in his last 19 at-bats.
Cano's first home run made it 2-0 in the fourth, and successive doubles by Cano and Thames gave the Yankees a three-run cushion in the sixth.
Cano hit his eighth homer of the season in the eighth against Alberto Castillo. He has 17 career home runs against the Orioles, the most against any opponent.
NOTES: Cano also made a great defensive play at 2B, robbing Nolan Remold of a third-inning hit by grabbing a grounder up the middle and making a perfect throw to first from the outfield grass. ... Yankees C Jorge Posada was rested but available after being plunked in the right knee by a pitch on Wednesday night. ... Orioles RHP Koji Uehara (hamstring) pitched a scoreless inning for Double-A Bowie and will probably come off the 15-day DL next week.