A-Rod tied the major league record for home runs in April, hitting his 13th and 14th of the season in a 10-8 loss to the Tampa Bay Devil Rays on Monday night.
"This obviously is a tough time for us, but it's a long season. We've got to keep working ourselves out of it," Rodriguez said after the Yankees' fourth consecutive loss on a five-game road trip that ends Tuesday night.
"We need a win in the worst way. Again, I think hard work and grinding through it and supporting your teammates are the most important things."
Baldelli hit a three-run homer off Kei Igawa (1-1) in the second inning. Upton lined a solo shot off the left-field foul pole in the fourth for a 5-3 lead, then added a three-run double off reliever Luis Vizcaino to finish with a career-high four RBI.
"Against this team with their lineup, you've really got to hunker down inning by inning because they're going to keep coming at you," Devil Rays manager Joe Maddon said. "They're never out of the game, and it's never comfortable."
The Yankees, swept during a weekend series in Boston, got homers in the second and ninth innings from A-Rod, whose average rose to .400 after going 4-for-5 with three RBI and four runs scored.
The second-inning solo shot off Casey Fossum (2-1) was the 477th of Rodriguez's career and extended his hitting streak to 18 games to start this season and 23 in a row dating to last September. The two-run shot off Al Reyes in the ninth gave him 34 RBI, tied the mark for homers in April set by Albert Pujols in 2006 and broke the AL mark of 13 held by Ken Griffey Jr.
"What he's doing is amazing. I hope he keeps it up," New York's Johnny Damon said. "The whole team is rallying behind him. We can't wait until the next time he comes up."
But the Yankees, who have been beset with injuries, are off to an 8-10 start. Rodriguez said that makes it more difficult to enjoy what's he accomplished in the first three weeks of the season.
"It's easier to say `Wow' when we're winning games," he said. "The key is to not get discouraged. We've got to just keep the same approach, not try to do too much. If we can keep having that approach over the long haul, we'll have more wins than losses."
New York pitchers have given up six runs or more in five straight games and nine of 18 this season. In his fourth start since leaving Japan to sign with the Yankees, allowed seven runs and eight hits in 4 1/3 innings.
"You know it's going to get better. We're a team. We win together. We lose together," Yankees manager Joe Torre said. "Everybody is playing their tails off. You go out there and score eight runs, it certainly should be enough. We just haven't been able to make it."
Rodriguez lined a 2-2 pitch into the left-field stands off Fossum, who also yielded a solo homer to Robinson Cano in the fifth. The Devil Rays left-hander allowed six runs and 10 hits in 5 2/3 innings and benefited from the Yankees hitting into four double plays.
Derek Jeter singled in the seventh inning, giving him a 14-game hitting streak. He and Hideki Matsui, activated from the disabled list earlier Monday, drove in runs for the Yankees with sacrifice flies.
Tampa Bay loaded the bases in the seventh on a double and two walks. Upton doubled down the left-field line and all three runners scored easily.
"Our team should not lose four games in a row," Damon said. "It happens, but we're supposed to be better than this."
- Phil Hughes, the Yankees' top minor league pitching prospect, will make his major league debut Thursday against Toronto. The 20-year-old right-hander is 2-1 with a 3.94 ERA in three starts at Triple-A Scranton.
- To make room on the roster for Matsui, out since April 7 with a strained left hamstring, the Yankees optioned LHP Chase Wright to Double-A Trenton. Wright made his second big league start Sunday night and became the second major league pitcher to allow homers to four consecutive batters.
- Fossum has pitched in more games (19) against the Yankees than any other team. He's 5-4 in 10 career starts against them.
- NFL quarterbacks Chris Simms and Brian Griese threw out the ceremonial first pitches.