The Rams (15-2) advanced to the NFC title game for the second time in three years and will host the Philadelphia Eagles next Sunday.
"In all of my years of coaching, I don't know if I've ever seen a defensive performance like that," Rams coach Mike Martz said.
Favre's six interceptions tied a postseason record shared by three players, the most recent being Hall of Famer Norm Brocklin for Los Angeles in the 1955 NFL championship game against Cleveland.
"Not one of my better days," Favre admitted. "That was the most tipped balls that I've ever had. This one hurts, but I will be back."
"He's had a helluva year and today wasn't one of his best days. He would be the first to admit that," Packers coach Mike Sherman said of his quarterback. "We have received a lot of benefits of his good days and obviously, today wasn't one of his best ones."
This marked the first-ever duel between Favre and St. Louis' Kurt Warner -- the quarterbacks who have combined to win five Most Valuable Player awards.
But it was the overhauled defense of the Rams, especially Williams and rookie linebacker Tommy Polley, which seized the spotlight and outscored the Packers, 21-17.
Williams played just two playoff games in 10 years with the Arizona Cardinals before he was acquired by the Rams last April as perhaps the most important move in their defensive transformation under coordinator Lovie Smith.
On Sunday, Williams became the first player to return two interceptions for touchdowns in a postseason game. He opened the scoring with a 29-yard return 5:49 into the game and capped the rout with a 32-yard touchdown with 7:50 left. He also stripped the ball from Antonio Freeman and recovered the fumble, figuring in three of the Packers' eight turnovers.
"It feels great," Williams said. "All the focus was on the offenses, but we know how much defense means in the playoffs. As a team, we can win games many different ways."
"That was one for the record books -- two interceptions for two TDs and almost had a fumble for a TD," Martz said of Williams.
Polley, who assumed the starting outside linebacker position last month, had two interceptions and scored on a 34-yard return as the St. Louis defense matched its prolific offense with three touchdowns.
Overshadowed by Warner, his arsenal of receivers and 2000 MVP Marshall Faulk, the Rams' defense changed eight of 11 starters and ranked first in the NFC.
"We've got some guys on defense that don't really get the notoriety," Faulk said. "They don't get recognized for the things they did (during the season), but when you perform on the big stage like they did today, it will come."
Warner, the MVP this season and in St. Louis' Super Bowl campaign in 1999, threw for 216 yards and two scores with one interception. He had been bothered by a throat contusion suffered in the regular-season finale but had no problems barking out the signals Sunday.
"I deserved to get cut then," said Warner, who persevered and starred in the Arena League from 1995-97 and played in NFL Europe before joining the Rams in 1998. "I'm a much different player now than I was then and everything worked out for the best."
A three-time MVP, Favre completed 26-of-44 passes for 281 yards and two TDs for the Packers (13-5). But his six interceptions accounted for 161 yards for the Rams.
A 45-yard interception return by safety Kim Herring, a starter on Baltimore's record-setting defense last season, set up a four-yard scoring toss from Warner to fullback James Hodgins. Herring also forced a fumble and cornerback Dexter McCleon had St. Louis' other interception.
Green Bay which was plus-12 in takeaway-giveaway ratio during the season, fell one shy of tying a postseason record for most turnovers in a game.
"It's hard to beat a Pop Warner team with eight turnovers, let alone the St. Louis Rams," Freeman said.
The first came when Favre and receiver Bill Schroeder miscommunicated on a pattern. Favre threw a short pass that went right into the arms of Williams as Schroeder ran upfield. Williams raced 29 yards untouched to give the Rams a 7-0 lead.
Green Bay's next possession resulted in another turnover when Ahman Green fumbled after being hit by Herring at the end of a 15-yard run. Rookie safety Adam Archuleta recovered for the Rams at their own 35.
Favre quickly went to work, hitting Corey Bradford and Donald Driver with passes of 27 and 16 yards, respectively. Three plays later, Freeman turned a short pass into a 22-yard touchdown, tying it at 7-7 with 2:35 left in the first quarter.
The Rams wasted no time responding as Warner hit Az-Zahir Hakim with a 15-yard pass and Faulk broke off a 38-yard run to the Green Bay 11. Two plays later, Warner found Torry Holt for a four-yard TD on a quick slant two seconds into the second quarter.
On Green Bay's ensuing possession, Herring picked off a pass intended for Freeman and returned it 45 yards before he was pushed out of bounds at the Packers' 4.
Two plays later, Warner connected with Hodgins for a four-yard touchdown 2:24 into the quarter, increasing the lead to 21-7.
Allen Rossum thought he returned the ensuing kickoff 95 yards for a touchdown, but the play was called back due to a holding penalty on rookie Torrance Marshall.
Ryan Longwell kicked a 28-yard field goal for Green Bay with 4:18 left in the half, but Jeff Wilkins responded with a 27-yarder for the Rams with 21 seconds remaining.
St. Louis scored two touchdowns in a 92-second span in the third quarter to open a 38-10 lead.
On Green Bay's first possession of the second half, Green broke off a 49-yard run. However, on 3rd-and-6, Freeman caught a short pass and had the ball stripped by Williams, who fell to the ground at the St. Louis 31, got back on his feet and raced to the end zone. A replay challenge showed Williams was down by contact, negating the touchdown.
Three plays later, however, Warner and Holt connected on a 50-yard pass to the Green Bay 7.
"It was one of the few big plays on offense," Warner said of the bomb to Holt. "I think from that point on, we were able to get some points and separate."
Faulk, who finished with 82 yards on 16 carries, went around left tackle on the next play for a seven-yard touchdown 5:16 into the third quarter.
On Green Bay's next possession, Favre had a pass deflected by end Grant Wistrom into the hands of Polley, who brought it back 34 yards for a score with 8:12 left in the period.
Williams punctuated his performance with a 32-yard interception return for a score on a pass that went off the hands of Green.
"Sometimes his receivers miss those torpedoes he throws," Williams said of his second interception.
"He's one of the best I've faced, but I wouldn't say he is the best," Favre said of Williams. "I've faced Deion Sanders before. But (Williams) is definitely one of the best."
Favre hit Freeman with an eight-yard touchdown with 5:46 remaining.