Rodriguez's single to right scored Rick Ankiel to cap a two-run rally. Pinch-runner Brian Bixler had tied the game on a double steal, taking third and then coming home when catcher Eric Fryer's throw went into left field for an error.
In the first game, Garrett Jones and Andrew McCutchen hit back-to-back homers in the eighth inning, and James McDonald had a strong outing in the Pirates' 5-3 victory. That win put Pittsburgh two games over .500 for the eighth time this season, but they are now 0-8 trying to get to three above the break-even mark.
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The doubleheader was Pittsburgh's first in Washington since they split with an early incantation of the National League Senators at Boundary Field on May 19, 1899. McCutchen marked the occasion by hitting for a "doubleheader cycle" -- home run and double in Game 1; triple, double and single in Game 2.
Until the late comeback in Game 2, the theme of the day for the frustrated home fans was the Washington's ongoing offensive woes. Slumping high-priced outfielder Jayson Werth batted fifth for the first time this season in the second game, but it didn't help. He went 0 for 3 with two strikeouts, was booed multiple times and doffed his helmet toward the fans after flying out in the eighth. The player with the seven-year, $126 million contract is hitting .165 since June 1.
Ryan Mattheus (1-0) pitched the eighth inning to get the win in Game 2, and Drew Storen handled the ninth for his 20th save.
Tony Watson (0-1) took the loss in the nightcap for the Pirates.
Pittsburgh's Brad Lincoln, recalled from Triple-A Indianapolis to pitch the second game, allowed two runs over six innings in his season debut.
The split gives Davey Johnson a 2-4 record since becoming Washington's manager.
Livan Hernandez and John Lannan became the latest Nationals starters to have a good outing go to waste. Hernandez allowed two runs and six hits over seven innings -- the first earned runs allowed by Washington's pitching staff in three games -- but didn't get the decision in the opener. Lannan gave up three runs and six hits over seven innings in the second game.
The opener was tied at 2 when Jones and McCutchen took Sean Burnett (3-5) deep in the eighth. Jones entered the game hitting .129 against lefties, with no homers and two RBI, but he took the lefty reliever the opposite way and put one into the red seats in left center. Burnett had only allowed one home run all season.
"It definitely feels good to get one off a lefty. I've been struggling off them," Jones said. "I saw the ball well today, just trying to make strides and stay close and stay in a big part of the field, stay up the middle and left-center off the lefty - and was able to stay on that one good."
McDonald and Hernandez dominated much of the game, combining for 13 strikeouts and six 1-2-3 innings. McDonald allowed two runs and seven hits over 6 1-3 innings before giving way to Jose Veras (2-2), who pitched 1 2/3 innings to get the win.
"My preparation was a little different this time. My 'pen was a lot more focused, more game-like attitude to bear down on hitters and get that feel going," said McDonald, who decided on the new approach after a talk with pitching coach Ray Searage. "I feel like I carried my bullpen out to the game."
Joel Hanrahan gave up one run in the ninth but still got his 24th save in 24 chances this season, tying the club record for consecutive saves opportunities converted.
The Pirates placed SS Ronny Cedeno on the 7-day concussion disabled list. He was injured trying to break up a double play in Friday's game. Pittsburgh recalled INF Pedro Ciriaco from Triple-A Indianapolis. ... RHP Tim Wood was optioned to Indianapolis to make room for Lincoln. ... Pirates OF Xavier Paul, who had missed the last three games with tightness in his right hamstring, entered the first game in the eighth inning. ... After Friday night's win, Johnson asked reporters for directions to his new home in the nation's capital, having yet to make the drive there from Nationals Park. Asked on Saturday if the trip went OK, he said it did - despite an apparent wrong turn on an interstate. That led to a long discussion about the city's notorious traffic. "If push comes to shove," he concluded, "I really know how to walk out there and get a cab." ... Nationals reliever Henry Rodriguez was unavailable because of strep throat. ... Nationals RHP Chien-Ming Wang made his second rehab start Saturday, throwing four scoreless innings at for Single-A Potomac.