Josh Judy gave up two runs in the bottom of the ninth, but still nailed down the save for Zach Putnam, who earned the win by pitching two perfect innings of relief.
Jerad Head had three hits, while Rodriguez, Jose Constanza and Matt McBride had two apiece for the Aeros, who jumped out to a 3-0 lead.
Aeros starter Jeanmar Gomez, the EL Pitcher of the Year, was not real sharp, but kept Akron in the game. The right-hander allowed two runs and six hits over five innings, walking three and striking out five.
Carlton Smith then gave up three walks, one hit and two runs over only one inning.
But Akron's offense was as good as it has been all season. The Aeros strung together four hits to take a 3-0 lead in the third inning.
John Drennen, who has been on a hot streak since the last week of August, singled up the middle. Head, who drove in eight runs in Akron's three-game sweep of Reading in the first round, then doubled home Drennen and went to third on a throwing error.
Constanza grounded a single to left to score Head and went to third on a single up the middle by Rodriguez.
After league MVP Carlos Santana popped out, Beau Mills reached on a fielder's choice as the speedy Constanza beat the throw home for a 3-0 lead.
Head doubled in the seventh and scored on a single by Santana for a 4-2 lead.
After the Defenders tied it in the bottom half, the Aeros put it away in the ninth.
Head hit a leadoff triple, but didn't score on a ground ball by Constanza -- who beat it out for a single. Rodriguez then lined his first homer of the playoffs to center for a 7-4 lead.
Akron, in the best-of-five finals for the fifth straight year, is seeking its first title since 2005. The Aeros won the Southern Division by 14 games in the regular season and had a three-game sweep in the first round of the playoffs.
The Aeros lost to Trenton in the finals in 2007 and 2008 and fell to Portland in 2006 after winning the title in 2005.
That 2005 team went 86-56 during the regular season, beat Altoona in five games in the first round and Portland in four games in the finals. It included such future major-league players as Jeremy Sowers (5-1, 2.08 ERA); Rafael Perez (4-3, 1.76 ERA); Fausto Carmona (6-5, 4.07 ERA); Ben Francisco (7 homers, 15 steals, .307); Franklin Gutierrez (11 homers, 14 steals, .261); Jon Van Every (27 homers, .244); Michael Aubrey, Eider Torres, Ivan Ochoa, Tom Mastny, J.D. Martin, Edward Mujica, Brian Slocum and others.