GREEN BAY, Wis. -- Packers quarterback Aaron Rodgers nearly came up six throws short of the NFL record for the most consecutive pass attempts without an interception. But after Atlanta Falcons linebacker Deion Jones dropped a ball that practically hit him between the numbers on his jersey, Rodgers successfully threw on.

On his third pass attempt of the second half, he tied Tom Brady's NFL record with his 358th straight pass without an interception. On his next throw, he broke it.

Rodgers' 359th consecutive pass without an interception was a 24-yard touchdown to Randall Cobb to give the Packers a 27-7 third-quarter lead over the Falcons en route to a 34-20 victory.

Rodgers came into the game needing 22 attempts without a pick to tie Brady. The dropped interception by Jones in the second quarter was his 16th pass of the game. Rodgers finished with his streak intact at 368.

Rodgers said that on a streak as long as his, there'll be some close calls like the one he had with Jones today.

"That happens from time to time when you get a good streak of interception-free passes, there's going to be a couple [of near misses]," said Rodgers, who was 21-of-32 for 196 yards with two touchdowns. "We had one against Arizona last week where [Marquez Valdes-Scantling] kind of broke out and I was throwing break in. Obviously it was cold and a little bit damp, the guy drops it. [Jones] had a couple chances. One, Jimmy [Graham] kind of backed into the route a little bit on a sit over the ball. And the other one, I was thinking Jamaal [Williams] was going to kind of go up and back, and he kind of sat there. [Jones] wasn't looking and then right at the last second, thankfully, he took his eyes back but didn't get a great look at it the whole time. You need a little bit of good fortune when you have a streak like that."

Rodgers' last interception came in Week 4 against the Buffalo Bills on a twice-deflected pass. It's Rodgers' only interception of the season. He threw his 22nd touchdown of the season in the first half to Davante Adams (for Adams' 11th TD catch of the season).

Rodgers came into the game ranked first in NFL history in touchdown-to-interception ratio (4.22) among quarterbacks with at least 1,500 pass attempts.

Brady set the interception-free record during the 2010 and 2011 seasons.