Jones homered on the first pitch from Fernando Rodney (0-1) in the 11th after the Twins threatened against Richard Bleier (1-0) in the top half of the inning.
Earlier, Caleb Joseph lined a two-run triple with two outs in the bottom of the seventh inning to give the Orioles a 2-0 lead.
The Orioles got some help from Minnesota relief pitcher Zach Duke in that inning. He struck out Trey Mancini to start the inning but let the left fielder reach on a wild pitch.
Duke threw a second wild pitch that moved Mancini to second. After Tim Beckham struck out, and pinch hitter Danny Valencia was intentionally walked, and Duke got his third strikeout of the inning when he set down Craig Gentry.
However, the inning went on, and that's when Joseph lined his shot to right-center that scored both Mancini and Beckham for the two-run lead.
Darren O'Day set down the Twins in order in the eighth before they rallied in the ninth versus Brad Brach. Minnesota loaded the bases with two outs before pinch hitter Robbie Grossman tied it with a two-run single to short center field.
Brach threw 34 pitches but blew his first chance at a save as he's filling in for closer Zach Britton, out for at least two months after surgery for a torn Achilles tendon. Mychal Givens came on to get the final out in the ninth.
Both teams wasted good work from their right-handed starters. For Baltimore, Dylan Bundy (1-0) scattered five singles in seven shutout innings and threw 88 pitches -- 64 of which were strikes.
Jake Odorizzi threw six solid innings in his Minnesota debut. He was acquired in a spring training deal with Tampa Bay and gave up only two hits while striking out seven and not allowing a run.
However, the Twins could not give Odorizzi any offensive support despite the five hits in seven innings off of Bundy.
Still, they nearly took the lead in the second when Eddie Rosario hit a fly ball to deep right but Gentry made a leaping catch at the fence, bringing the ball back over the top and keeping the game scoreless.
The victory improved Baltimore to 8-0 on Opening Day under manager Buck Showalter.
--Field Level Media
Minnesota | Baltimore | |
Jake Odorizzi | Player | Dylan Bundy |
No Decision | W/L | No Decision |
6.0 | IP | 7.0 |
7 | Strikeouts | 7 |
2 | Hits | 5 |
0.00 | ERA | 0.00 |
Minnesota | Baltimore | |
Robbie Grossman | Player | Manny Machado |
1 | Hits | 2 |
2 | RBI | 0 |
0 | HR | 0 |
1 | TB | 3 |
1.000 | Avg | .500 |