The Packers stretched their NFL win streak to seven games by ripping the New York Giants 38-13 as Rodgers threw for 362 yards and four TDs
Aaron Rodgers matched a Green Bay playoff record with four touchdown passes Sunday while Le'Veon Bell ran for a Pittsburgh playoff record 167 yards and two touchdowns to spark first-round home routs.
The Packers stretched their NFL win streak to seven games by ripping the New York Giants 38-13 as Rodgers threw for 362 yards and four TDs.
Also matching a one-game Packers mark was Randall Cobb, who hauled in three touchdown throws, including a spectacular "Hail Mary" desperation toss to end the first half.
"We hit a 'Hail Mary' -- that got us going," Rodgers said. "We got going really well. We're better with 18 (Cobb) on the field and he showed it tonight."
Pittsburgh's Ben Roethlisberger connected on two touchdown tosses to Antonio Brown in addition to Bell's heroics as the Steelers humbled Miami 30-12.
"Those guys up front did a great job opening holes for me," Bell said. "It was a total team effort. I just ran hard and picked my spots."
Green Bay booked a second-round matchup next Sunday at Dallas. The Packers lost at home to the Cowboys 30-16 last October.
"Can't wait," Rodgers said.
The Steelers booked a second-round game next Sunday at Kansas City. Pittsburgh routed Kansas City 43-14 in October but this time the Chiefs will play at home.
"We kind of gave it to them last time so they're going to come in with the mindset not to let that happen again," Bell said. "We've got to step up and play our best."
Pittsburgh's victory also sent the Houston Texans to season-wins leader New England next Saturday, the same day Seattle will visit Atlanta in the other second-round playoff game.
Roethlisberger, who connected on 13 of 18 passes for 197 yards, suffered a right ankle injury late in the game but vowed "I'll be out there next week."
Bell broke the old Steeler one-game playoff rushing mark of 158 yards by Franco Harris against Minnesota in the 1975 Super Bowl.
Each game was played in bitter cold with wild chills near 2 degrees F (minus-16 degrees C).
At Green Bay, New York's Robbie Gould kicked field goals of 26 and 40 yards to give the Giants a 6-0 lead, but dropped passes thwarted the Giants' touchdown bids.
The Packers, who lost top receiver Jordy Nelson to a rib injury early in the game, answered 2:20 before halftime when a scrambling Rodgers, behind solid blocking, eluded onrushing defenders before finding Davante Adams on a 5-yard touchdown pass, with the conversion kick putting Green Bay ahead.
Rodgers saved his greatest magic for the final play of the first half, hurling a long throw that Cobb grabbed in the back of the end zone for a 14-6 Packers halftime lead.
Cobb had raced downfield and worked his way behind six leaping New York defenders to find himself in perfect position for the catch to complete the stunning play.
The Giants responded in the third quarter, the defense stopping Green Bay on downs to take possession and set up Eli Manning's 41-yard touchdown pass to Tavarres King, pulling New York within 14-13.
Green Bay answered just five plays later, with Rodgers throwing a 30-yard touchdown to Cobb to extend the lead and Mason Crosby added a field goal for a 24-13 Packers lead entering the fourth quarter.
Rodgers threw a 16-yard touchdown pass to Cobb and Aaron Ripkowski scored on a 1-yard touchdown run to stretch the final margin.
Chilly Pittsburgh was a far cry from the Miami warmth in which the Dolphins beat Pittsburgh 30-15 in a regular-season game.
"Big Ben" connected with Miami native Brown on touchdown throws of 50 and 62 yards to give the Steelers a 14-0 lead with only 8:10 elapsed.
Miami's Andrew Franks kicked a 38-yard field goal but Pittsburgh answered on Bell's 1-yard touchdown run, followed by Franks adding a 47-yard field goal for the Dolphins trimming the Steeler lead to 20-6.
Mike Mitchell forced a third-quarter fumble by Miami quarterback Matt Moore and L.T. Walton recovered for Pittsburgh, setting up Chris Boswell's 34-yard field goal.
Pittsburgh's Ryan Shazier intercepted Moore's next pass and that led to an 8-yard Bell touchdown run, Pittsburgh's lead growing to 30-6.
Moore flipped a final 4-yard touchdown pass to Damien Williams with 5:57 remaining, but missed on a two-point conversion throw.