Manager Joe Maddon then flip-flopped the pair, both of whom are fighting for the starting shortstop job this spring, after three innings.
Both have also been out of the lineup lately -- Rodriguez because of his finger, Brignac for the birth of his son and, separately, a stomach problem.
"We want to get them back on the field at the same time and playing," Maddon said. "The fact they're both comfortable at second base allows us to get at-bats for both of them."
Rodriguez entered the spring as the favorite to win the job based on his strong finish to the 2011 season. However, Brignac has shown some improvement.
"Reid's working better at-bats," Maddon said."He's swinging at better pitches. ... [He's] running the bases pretty well, bunted well the other day. That's why I believe our meetings are so invaluable at the beginning of camp. A lot of the things we've spoken about [to Brignac], it's apparent he's really listened. I've seen some improvement in different areas.
"He's on track. It's really early to say that he's accomplished all these different things. But he's definitely moving in the right direction. Among all the guys, he's probably near the top of working on that list and doing a good job of it."