Mia Cooper, who finished with seven points and six rebounds, sank two free throws with 4.1 seconds left to put McEachern (24-6) on top 56-53.
Hillgrove (22-6) let the ball roll near midcourt on the inbounds play, but the clock inadvertently started early, forcing the Lady Hawks to replay the ball.
McEachern took advantage of the restart and played a fullcourt press the second time around, forcing Rodrigo to put up the last-second heave.
"I was just saying the biggest prayer that Mia would make those free throws," said McEachern coach Phyllis Arthur, who will guide the Lady Indians into their first semifinal since 2005. "If she makes those, the best Hillgrove could do was send it into overtime.
"I knew that free throws would be key coming into this game. I told the girls that over and over and they listened and they believed."
McEachern went 19-for-27 from the line overall, but shot 10-for-12 in the fourth quarter and 7-for-8 in the final 3 minutes.
Now the Lady Indians McEachern will await Mill Creek in Thursday's 7 p.m. semifinal at the Arena at Gwinnett Center.
Leading 44-35 with 5:22 left in the game after Cooper drained a 3-pointer, Reka Hall hit a jumper to spark a 9-1 run for the Lady Hawks run.
Hall finished the game with 19 points, including 11 in the fourth quarter, and added five rebounds and five steals
Meredith Heyer's 3-pointer at the 2:51 mark then capped the spurt as Hillgrove trailed 45-44.
The margin stayed at one, 54-53, after Mackenzie Engram hit a jumper with 20.8 seconds on the clock, setting up Cooper's final free throws with seconds remaining in the game.
The win gave McEachern its third win over Hillgrove in three games this season.
"We changed up our game plan on them after we lost the first two times," Hillgrove coach Sheryl Fowler said. "We backed down into the paint and didn't play as much (man-to-man). We threw some junk defenses at them, and when they spread the floor because they had the lead, we had to play man. Our goal was to try to keep them on the outside."
Hillgrove led 11-10 at the end of the first quarter, but McEachern took control 26-23 at halftime and extended the margin to 37-31 at the end of the third period.
Much of the credit went to Dominique Wilson, who finished with 18 points, three assists and two steals. Wilson directed the offense and hit a layup with 30 seconds remaining in the game to give the Lady Indians a 54-51 advantage.
"I told Dominique before the game that I wanted this to be of the biggest games she's played in her career," Arthur said. "I'm proud of this team for playing so hard."
Brittany Hodges had 13 points, including 11 in the second half, to go with five rebounds.
Hillgrove trailed by two points or less on seven occasions in the fourth quarter, but couldn't get over the hump. The Lady Hawks negated much of McEachern's size in the frontcourt by using 6-foot-1 freshman Engram and 5-11 junior forward Tiffani Schick.
"There wasn't a whole lot to say to the girls after this," Fowler said. "They battled hard and we had a great season. I'm really proud of them. They didn't quit and left it all on the floor."
Rodrigo, finished with 14 points - 10 in the second half - for Hillgrove along with four assists and four steals. Heyer had eight points, including two 3-pointers, and Engram totaled five points and seven boards. Bria Smith added five points and five rebounds.
Kayla Montgomery chipped in 12 points and eight rebounds for McEachern, while Pachiyaanna Roberts contributed six points and four boards.