A half-inning earlier, Phillips turned in a nifty defensive play. Running up the middle, he stabbed at Chris Denorfia's grounder and in one motion, jumped, turned and threw to first base for the out.
''Had some really good defense, especially early with Brandon and (third baseman) Todd Frazier,'' Cincinnati manager Bryan Price said. ''Some nice plays there.''
Jay Bruce went 2 for 2 with a triple. Cozart had two hits, scored three times and stole a base, and Donald Lutz homered in the ninth.
Reds starter Brett Marshall threw two scoreless innings. The Padres didn't get a hit until the sixth inning.
''Nice to see Jay swing the bat so well,'' Price said. ''A lot of well hit balls today. It was just good to see.''
Cincinnati: Marshall walked two and hit a batter, while striking out one and being credited for the win. He threw 25 pitches in his outing - 13 for strikes - and induced two double plays.
''It was also nice to see Brett Marshall come in there and throw the ball well,'' Price said.
San Diego: Tyson Ross tossed two shutout innings, allowed no hits, one walk with one strikeout in his first spring training appearance.
Cincinnati: Pitcher Mike Leake was supposed to make his first start of spring training against San Diego, but the right-hander was scratched because of an abdominal injury. The date of his next start has not been set.
Reds speedster Billy Hamilton showed some timely hitting when he doubled home Roger Bernadina in the third inning for his first RBI of spring training.
But his first at-bat offered intrigue, too, even though it ended up with Hamilton grounding out to first base. A threat to steal whenever he gets on base, Hamilton has struggled to get there - his OBP was .308 at Triple-A Louisville in 2013. The Reds' leadoff hitter saw nine pitches in his first at-bat, and after starting the count 0-2, he took a ball, fouled off three straight pitches and took two more balls before grounding out.
Hamilton is hitting .286 in three spring starts.
SPRING DEBUTS: San Diego right fielder Chris Denorfia and designated hitter Will Venable made forgettable spring training debuts Sunday. Denorfia went 1-for-3, while Venable was 0-for-2 with a walk.
On Monday, pitcher Josh Johnson will make his first start with the Padres when he faces San Francisco in Scottsdale, Ariz. Johnson signed a one-year contract with San Diego in November.
THIS AND THAT: Frazier tallied his first hit, run and stolen base of spring training for Cincinnati. ... For San Diego, Sunday was the only day of spring training that the Padres will have split-squad games. ... In addition to the 3,311 people in attendance, 112 dogs occupied Peoria Sports Complex as part of an Arizona Humane Society promotion.