ET caught up with the would-be-couple just before the film hit theaters, which was also the start of their steamy relationship.
"We're very competitive," Jolie revealed at the film's junket.
"She might say so. I didn't feel much competition," Pitt cracked.
Jolie and Pitt's on-screen characters were very similar in that respect.
"What I like about it most [is that] the relationship or the argument's in the foreground," the Ocean's Eleven star shared. "The action's always in the back. It always supports whatever they're fighting about."
"There's not really a love scene in there," he added. "I know you wanna make something out of it, but there's really not."
While the two played coy on their budding romance, Jolie admitted to developing feelings of "trust" with Pitt.
"This is the first time I had a kind of pairing, even when it came to the fight scenes -- it was coordinated with this other person," Jolie said. "Trust and the ability to throw something and catch it, you're not on your own. It was nice to learn about how fun that can be and how much easier that can be than being on your own."
The couple continued to keep their relationship under wraps until Pitt and his then-wife, Jennifer Aniston, had separated in January 2005. Two years later, however, Jolie did open up on how well she and Pitt connected while filming Mr. & Mrs. Smith.
"Brad was a huge surprise to me. I, like most people, had a very distant impression of him from... the media," she told Voguein 2007. "We were both living, I suppose, very full lives... I think we were the last two people who were looking for a relationship. I certainly wasn't. I was quite content to be a single mom."
"Because of the film, we ended up being brought together to do all these crazy things, and I think we just found this strange friendship and partnership that kind of just suddenly happened. I think a few months in I realized, 'God, I can't wait to get to work,'" she continued. "Anything we had to do with each other, we just found a lot of joy in it together and a lot of real teamwork. We just became kind of a pair."
All that time together eventually led to a lot more than simply friendship.
"It took until really the end of the shoot for us, I think, to realize that it might mean something more than we'd earlier allowed ourselves to believe," Jolie explained. "And both knowing the reality of that was a big thing, something that was going to take a lot of serious consideration."
Pitt has also admitted to falling for Jolie while filming the action flick. In a 2008 interview with Rolling Stone, he said that Mr. & Mrs. Smith was his favorite Jolie film "because, you know... six kids. [It's my favorite] because I fell in love."