GREEN BAY, Wis. -- The NFL, as part of its Super Bowl 50 celebration, billed Monday night's game between the Green Bay Packers and Kansas City Chiefs as a Super Bowl I rematch.

This game wasn't much more competitive.

Aaron Rodgers threw five touchdown passes, including three to Randall Cobb, as the Packers rolled over the Chiefs 38-28 at rainy Lambeau Field.

The Chiefs, coming off a mini-bye week following last Thursday's shocking loss against Denver, were outclassed in every way imaginable while falling behind 38-14 early in the fourth quarter. At halftime, Rodgers had more touchdown passes (three) than counterpart Alex Smith had completions (two).

"I just think we're scratching the surface a little bit," Rodgers said of the 3-0 Packers. "It starts with the guys up front. They've been blocking really well. We have three games in, we've got three sacks. That's pretty impressive. If those guys keep blocking like that we're going to be tough to beat."

Kansas City put an end to one ugly streak as it tried to dig its way out of a deep hole in the second half. When Smith hit Jeremy Maclin for a 5-yard touchdown late in the third quarter, it was the Chiefs' first touchdown pass to a wide receiver since the playoff loss to Indianapolis on Jan. 4, 2014 -- a streak of 18 consecutive games.

"The one positive," Smith said. "It is nice to get the ball in his hands and get him in the end zone. We won't have to deal with the receiver talk anymore."

However, the Chiefs (1-2) repeatedly shot themselves in the foot. The Packers gained five first downs via Chiefs penalties in the first half alone. Early in the fourth quarter, Rodgers drew the Chiefs offside again and, as he has done repeatedly through the early part of the season, took advantage of a free play by hitting James Jones for a gain of 52. That put the Packers in position for Cobb's career-high third touchdown reception of the night, which put Green Bay in front 38-14.

"That's a really good defense," Cobb said. "They have a really good pass rush. Our O-line played really well. Aaron had plenty of time to get the ball out and we were able to make plays down the field."

Since 2010, Rodgers has four games of five-plus touchdowns. Only Drew Brees (five) has more. Jones had seven catches for 139 yards and Cobb had seven for 91.

Maclin's 61-yard, bobbling catch-and-run set up Jamaal Charles' second touchdown run. On the first, Charles imitated Rodgers' "championship belt" celebration. On the second, he did a Lambeau Leap. That touchdown, and a two-point pass to Travis Kelce, brought the Chiefs within 38-22 with about 10 minutes remaining. Charles' third touchdown, a 7-yard run in which he ran over linebacker Joe Thomas, kept the Chiefs alive with 1:25 to play. However, Smith, who threw for 251 yards in the second half, misfired on the two-point play to Jason Avant, keeping it a two-score game at 38-28.

If there were any thoughts that the Packers might be feeling a bit too good about themselves following last week's emotional win over Seattle, they quickly were extinguished as they rolled to a 24-7 halftime lead.

After both teams exchanged punts, Green Bay had scoring drives of 69 and 89 yards to take a 14-0 lead in the game's first 13 minutes. A 26-yard gain by Eddie Lacy on a screen preceded Rodgers' 8-yard touchdown pass to Ty Montgomery for the opening points. On the second scoring drive, the Chiefs handed the Packers three first downs via penalties -- including a 12-men-on-the-field infraction on third-and-1. Another big gain on a screen, this time a 19-yarder by James Starks, set up Rodgers' 3-yard touchdown pass to Cobb.

Kansas City briefly turned the tide early in the second quarter. The Packers drove to the Chiefs' 39 but, on fourth-and-5, Tamba Hali's pressure forced an incomplete pass. The Chiefs barely needed a minute to get into the end zone, with a 38-yard catch-and-run by Kelce setting up Charles' 9-yard touchdown run.

Green Bay responded with a field goal, though an illegal-contact penalty by Marcus Cooper erased a sack-strip by Allen Bailey that was recovered by Hali. Hali, however, put the brakes on the drive with a third-down sack.

Two more penalties killed the Chiefs just before halftime. First, on third-and-1, Rodgers rushed the offense to the line of scrimmage and again caught the Chiefs with 12 on the field. On the next play, Rodgers drew Hali offside and fired a 27-yard touchdown pass to James Jones.

"All in all, that is my responsibility," Chiefs coach Andy Reid, repeating the same basic words again and again. "The whole thing here, offensively and defensively, was my responsibility."

NOTES: Packers WR Davante Adams, who missed past of last week's game with a sprained ankle, aggravated the injury on the first series and did not return. ... Chiefs CB Phillip Gaines sustained a knee injury in the first quarter and did not return. ... The Packers outgained the Chiefs 150-3 in the first quarter and 304-94 in the first half, with Aaron Rodgers passing for 208 yards compared to Alex Smith's 39 ... Chiefs LB Derrick Johnson broke Gary Spani's club record of 999 tackles for his career. Early in the third quarter, Johnson had totaled 1,000 for his career. ... The Packers honored the Super Bowl I team that beat the Chiefs 35-10.... Chiefs OLB Justin Houston's streak of eight consecutive games with at least one sack came to an end. ... The Packers' streak of games with at least one sack reached 39, with Alex Smith dropped seven times.