NEW YORK — Daryl Thompson woke up early Saturday, too excited to sleep. His major league debut just hours away, he joined two teammates for the subway ride to Yankee Stadium, got lost and ended up in Brooklyn.

‘‘That’s why I got here late,’’ Thompson said. ‘‘Kind of a bad impression, you know, first day.’’

Thompson made quite the impression once he arrived, working out of a couple of jams in five innings to lead the Cincinnati Reds to a 6-0 victory over the New York Yankees.

‘‘It was nice,’’ said Ken Griffey Jr., who had two hits and scored two runs. ‘‘He held his own out there.’’

Edwin Encarnacion’s two-out, two-run single off Dan Giese (1-2) in the seventh gave Cincinnati the lead and Corey Patterson followed with a drive to right off Jose Veras for his 100th career homer. Brandon Phillips tacked on a two-run single in the eighth.

‘‘That was like a boxing match, momentum going back and forth,’’ Giese said.

Cincinnati has won the first two games in its first trip to the Bronx since it swept New York in the 1976 World Series.

Thompson and Giese locked up in the first matchup of pitchers making their first major league start at Yankee Stadium since Boston’s Tony Welzer faced New York’s Myles Thompson on April 22, 1926, according to the Elias Sports Bureau.

The Yankees put at least one runner on in eight innings and stranded 12. They’ve scored just four runs in their last three games.

‘‘You only get so many opportunities,’’ manager Joe Girardi said. ‘‘We had a lot of men on today and couldn’t score.’’

Bill Bray (2-0) followed Thompson with 1 1-3 innings, David Weathers got two outs and Jared Burton worked the eighth before Jeremy Affeldt finished the seven-hitter.

Giese made three relief appearances for New York and got the start Saturday when ace Chien-Ming Wang injured his right foot running the bases last Sunday in Houston.

He breezed through the Reds lineup early, getting through the first six innings in just 62 pitches. He was in good shape in the seventh, too, before his costly throwing error kick-started Cincinnati’s big inning.

Griffey led off the seventh with a single to center and Phillips followed with a grounder up the middle. Giese grabbed the ball and tried to retire Griffey but his throw pulled second baseman Robinson Cano off the bag.

‘‘It was just a bad throw,’’ Giese said. ‘‘There’s no excuse for it.’’

Griffey and Phillips moved up on Joey Votto’s groundout to third — with Griffey narrowly avoiding Alex Rodriguez’s tag attempt — and Giese struck out Adam Dunn for the second out. Encarnacion then chased the right-hander and put Cincinnati ahead 2-0 with a sharp single to left.

Giese allowed four hits and three runs, all unearned. He threw 53 of his 75 pitches for strikes.

Thompson allowed the leadoff hitter to reach in each of the first four innings and a two-out walk in the fifth but escaped unscathed each time. He allowed four hits, walked four and struck out two.

‘‘If you’re going to be a good pitcher, you’ve got to get out of trouble,’’ Reds manager Dusty Baker said. ‘‘Everybody’s going to get in it, but you have to have the fortitude and stuff to get out of it, which he showed today.’’

New York loaded the bases with no outs in the second against the 22-year-old right-hander, who bounced back in a hurry after a visit from Baker. Thompson struck out Jorge Posada, got Cano to foul out to catcher Paul Bako and fanned Melky Cabrera to get out of the inning.

‘‘To get out of that was a big thing for me,’’ Thompson said. ‘‘It boosted me up a lot.’’

Thompson, who was acquired by the Reds in an eight-player trade with Washington in 2006, leaped off the mound after Cabrera swung and missed at strike three.

‘‘We let him off the hook early,’’ Posada said. ‘‘We had a lot of guys on base and didn’t score.’’

Derek Jeter went 2-for-4 for the Yankees, extending his season-best hitting streak to 10 games. Jason Giambi also had two hits.

Notes: RHPs Darrell Rasner, Joba Chamberlain and Mike Mussina are scheduled to start in New York’s three-game series at Pittsburgh beginning on Tuesday night. Girardi said Giese would get another start in the Yankees’ doubleheader against the New York Mets on Friday but he wasn’t sure yet who would start the other game. … The Reds placed INF Jolbert Cabrera on the disabled list with a dislocated left index finger to make room for Thompson. … Cincinnati got RHP Gary Majewski, SS Royce Clayton, INF Brendan Harris, Bray and Thompson in the 2006 deal that sent OF Austin Kearns, SS Felipe Lopez and RHP Ryan Wagner to the Nationals. Majewski also is still with the team. … Two pitchers also made their first major league start at Yankee Stadium on May 6, 1962, but they didn’t oppose each other. Dave Stenhouse started for the Washington Senators in Game 1 of a doubleheader and Jim Bouton made his first start for the Yankees in the second game, according to Elias.