EMMITT SMITH ran for three touchdowns and Troy Aikman threw for two more as the Dallas, Cowboys earned their third Super Bowl berth in four seasons with a victory over Green Bay in the NFL play-offs. The Cowboys beat the Packers 38-27 in the National Conference championship game. ,They will meet the Pittsburgh Steelers, who beat the Indianapolis Colts 20-16 in the American Conference championship game earlier yesterday.

Smith carried the ball 35 times for 150 yards and scored on a one-yard run in the second quarter. His touchdown runs of five and 16 yards in the fourth quarter sealed the victory for Dallas, who will be appearing in their eighth Super Bowl. Aikman completed 21 of 33 passes for 255 yards and the touchdowns of six and four yards to Michael Irvin. Irvin caught seven passes for 100 yards.

Smith's second touchdown run of the game, a five-yard burst with 12:24 left, sent the Cowboys ahead, 31-27. Larry Brown intercepted a pass on the Packers' next drive and Smith sprinted 16 yards for his third touchdown with 9:28 left to make the score 38-27.

Regular season most valuable player Brett Favre's one-yard touchdown pass to Robert Brooks had given Green Bay a 27-24 lead over the Cowboys after three quarters.

Favre's third touchdown pass of the game was set up by a 54-yard pass play to tight-end Keith Jackson, who was pulled down at the Dallas one-yard line. Three plays later, Favre hit Brooks over the middle.

Smith had plunged over from the one with 24 seconds left in the second period to cap a 99-yard drive and give Dallas a 24-17 lead. Chris Jacke kicked a 46-yard field goal just 70 seconds into the game to give the Packers a 3-0 lead. Aikman's two short touchdown passes to Irvin gave the Cowboys a 143 lead in the first quarter.

The Steelers earned their ticket to the Super Bowl on January 28th by beating the Indianapolis Colts 20-16. Bam Morris plowed into the end zone from a yard out for the winning touchdown, 94 seconds from time.

The Steelers expunged the memory of last year's AFC championship game, when they came up three yards short against the San Diego Chargers.

For a few moments, they appeared on the verge of a similar upset, when Colts quarterback Jim Harbaugh threw a 47-yard touchdown pass to Floyd Turner with less than nine minutes remaining to give the underdog Colts a 16-13 lead. Steelers quarterback Neil O'Donnell responded by completing a 37-yard pass to Ernie Mills to the Colts one-yard line.

Morris' first attempt at the run failed. On the second he powered across the line, dragging Colts defenders with him. Still the Colts kept coming. Harbaugh piloted Indianapolis back down the field, and on the last play of the game lofted a failed Hail-Mary pass into the end zone toward Aaron Bailey, who was surrounded by Steelers.

Norm Johnson, who had a 31-yard field goal in the first quarter, kicked a 37-yard goal in the third to stretch Pittsburgh's lead to 13-9 going into the final quarter. He missed a 40-yard attempt with just under 11 minutes left that would have given the Steelers a seven-point advantage. Indianapolis took over after that miss and drove down-field to take the lead that yielded an exciting finish.

The Steelers have won four Super Bowls, but have not been to the NFL finale since the 1979 season, when they beat the Los Angeles Rams 31-19.