Rodriguez hit a solo home run in the first at-bat of his first rehab game in Tampa, Fla., on Friday night.
"For me, the home run meant a little bit more than a home run just because the last several weeks I was playing in New York I wasn't able to drive the ball," Rodriguez said. "I probably didn't hit a home run for like, over 70 at-bats."
Rodriguez, batting third as the designated hitter for the Yankees' Tampa affiliate in the Class A Florida State League, hit a pitch off of Dunedin's William Collazo over the wall in the top of the first.
"My team expects me to hit the ball and drive the ball out of the park," Rodriguez said. "That's what I expect out of myself, too. So hopefully I can come back and hit the ground running, and help my team win the division and go from there."
Rodriguez finished 2-for-3 with two RBIs.
"It's hard to be better than a homer and a double in three at-bats," Yankees manager Joe Girardi said Saturday afternoon. "That's a good sign."
He lined an RBI double off Collazo down the right-field line in the third. He took it easy running out the stand-up hit.
In his third and final at-bat, coming in the fifth against left-hander Matt Wright, Rodriguez struck out looking.
Rodriguez played the first of what is expected to be four minor league rehab games before rejoining the Yankees sometime during their seven-game, seven-day road trip next week.
"Just making sure that we take it one step at a time," Rodriguez said after the game Friday. "We've got about five or six days here to work with, and my idea is to always to ramp it up and hopefully keep increasing the intensity."
He could be activated as soon as Thursday, according to ESPN The Magazine's Buster Olney.
Rodriguez will play another minor league game for Tampa on Saturday, and will take part in a simulated game on Sunday.
On Monday, he'll travel to Triple-A Scranton and play at least two games there, on Tuesday and Wednesday.
Yankees GM Brian Cashman called that schedule a "preliminary plan" and said it would happen "weather permitting."
Olney reported that the Yankees want Rodriguez to play two full nine-inning games at third base before he's activated.
Assuming he gets through his minor league rehab stint without any setbacks, he'd likely be on track to come off the disabled list and rejoin the Yankees on Thursday.
"We hope so," Rodriguez said about returning next week. "You don't want to set anything for the record, but I think today was another step forward. Another day that I progressed pretty well and on target."
"If we have to work him back slowly -- to the point where he's playing four or five days in the field -- we can do that as well," Girardi said.
Rodriguez, who has been out since July 8 with a torn meniscus in his right knee that was surgically repaired July 11, will DH again on Saturday.
"I just got word (that he'll DH) from Cash," Girardi said. "He will probably just do situations at third Saturday."
Girardi wasn't concerned that Rodriguez wouldn't be getting game action at third base before heading to Triple-A Scranton.
"He could play a couple (games at third) in Scranton and be ready to go," Girardi said.
After this weekend's series with the Tampa Bay Rays, the Yankees travel to Kansas City for three games with the Royals beginning Monday night. Then they head to Minneapolis for four games with the Twins, beginning Thursday.
"Will we have him in Kansas City? I don't know," Girardi said before Thursday afternoon's victory over the Los Angeles Angels. "I would think by Minnesota we would have him.
"We'll have to build him up. I think the most important thing is that he feels comfortable and that he feels that he's moving freely."
At the time of his injury, Rodriguez was batting .295 with 13 home runs and 52 RBIs in 80 games.
Rodriguez still awaits a meeting with baseball officials about his alleged involvement in high-stakes poker games.
Major League Baseball started an investigation after Star magazine reported last month that several people saw Rodriguez playing in games hosted at Hollywood hotels and residences.
"I'm looking forward to (the meeting)," Rodriguez said Wednesday. "I'm concentrating on baseball."
No date for the meeting has been announced.
Mike Mazzeo and Ian Begley are frequent contributors to ESPNNewYork.com. Information from ESPN The Magazine's Buster Olney and The Associated Press was used in this report.