Greinke (1-0) began his Dodgers career by retiring the first five batters he faced. With two outs in the second, he gave up a hard one-hopper by Jones that second baseman Mark Ellis couldn't handle. The play was ruled a hit.
Greinke responded by setting down the next 14 hitters until McCutchen lined a single to center in the seventh. Mattingly swiftly made his way to the mound to take the ball from Greinke, who missed a couple of spring starts because of inflammation in his elbow and the flu.
"First impressions are important," Greinke said. "But I'm just trying to get one out at a time. No matter who it is, they're the most important batter at the moment. That's kind of what I do, and hopefully everything takes care of itself."
Greinke got some help from his defense, particularly shortstop Justin Sellers in the fifth. Sellers robbed Jones of a hit with a diving, backhand stab of a sharp grounder, bouncing up and throwing to first.
Brandon League pitched the ninth for his first save of the season, completing the two-hitter.
Sanchez was no stranger to the Dodgers, pitching against them for the 18th time in his career. All 17 previous appearances came with the Giants.
Like Greinke, Sanchez retired his first five hitters. But the sixth batter in the lineup, Ethier, drove a 2-2 pitch into the right-field bleachers.
Los Angeles broke through again in the sixth. After Ellis' leadoff walk, Kemp and Gonzalez hit back-to-back doubles to give the Dodgers a 3-0 lead, ending the night for Sanchez.
After Greinke came out in the seventh, Paco Rodriguez, Kenley Jansen and League combined to hold the Pirates hitless for the final 2 2-3 innings.
NOTES: Pirates catcher Russell Martin returned to Dodger Stadium for the first time since playing his final game with Los Angeles on Aug. 3, 2010. Martin, who spent the past two years with the Yankees after the Dodgers let him go following the 2010 season, received mostly boos from the crowd when he came to bat in the second inning. ... The Pirates went homerless for the fourth game in a row and remained the only National League team without a home run this season.