The Ravens raced into a 17-point lead at half time, but the Bengals came roaring back to force overtime with a last-second 51-yard touchdown from AJ Green.
However, the reigning Super Bowl champions recovered from the setback to score a winning field goal with 5:27 left in overtime, and Harbaugh was particularly delighted with the heart that his side showed.
"It's disappointment [conceding so late], but you don't get disheartened. You still have a chance to win the game," Harbaugh told the Associated Press.
"The thing is I'm most proud of is the heart of our guys. They showed the heart of champions. Where this will lead us, we'll find out."
The victory lifts the Ravens up to second in the AFC North, where they are now two wins behind the Bengals.