It was the Dallas Cowboys that led this change.
With the offensive line the Cowboys built, two different running backs led the NFL in rushing for a season. That's two NFL rushing leaders in a three year span.
The Cowboys offensive line was an elite run blocking machine that helped Demarco Murray break Jim Brown's 50 year record of consecutive 100 yard games to start a season. Murray had a hundred yard game in the first eight games of the 2014 season. In fact, he had ten 100 yard games in the first eleven games that season. He had 12 total for the 16 game season.
Two seasons later this offensive line protected a rookie quarterback who started every game that season. In addition, they led the way for a rookie RB to lead the league in rushing. The running game propelled these two rookies and their teammates to an 11 game winning streak.
How did they do this?
In 2013 the Cowboys defense was ranked 32nd in the league. As the 2014 season progressed, it became clear that the Cowboys best defender was their running game. It was efficient, They kept the ball driving downfield eating up the clock and keeping he opponent offense on the bench.
At the same time, it took pressure off Tony Romo. The Cowboys were rarely forced into having to throw the ball so Romo could just wait to take his shots. As a result, 2014 was the only season in which Tony Romo led all QB's in passer rating. Tony had averaged 565 pass attempts during the previous three seasons and only had to throw 435 passes in 2014.
By it's very nature, a productive run blocking scheme can compete with the prolific passing offenses because it limits their opportunities.
However, one of the greatest reasons for their success was the fact that teams had learned to build their defenses to stop the pass. That was the current trend in the NFL. Therefore, teams had built faster, but smaller front sevens in order to be more effective rushing the passer and covering receivers. Tyron Smith, Zack Martin, Travis Frederick, Ronald Leary, La' el Collins, and Doug Free plowed through these front sevens.
The Dallas Cowboys exposed the weakness of both the prolific passing offense and the defense designed to stop it.
They are the reason many current NFL teams are going back to more balanced attacks.