Lewis became the first NFL player to score on a kick-off return, pass and run in a play-off game.
His team will face Kansas or Pittsburgh next week for a Super Bowl place.
In Saturday's other match, the Atlanta Falcons made the NFC title game by beating the Seattle Seahawks 36-20.
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The Falcons, who had lost 26-24 at Seattle in the regular season, will play either Dallas or Green Bay on January 22 for a berth in the Super Bowl.
Lewis scored on a 98-yard kick-off return, caught a 13-yard touchdown pass from quarterback Tom Brady and ran for a one-yard touchdown in the final quarter.
Brady finished 18-of-38 for 287 yards with two interceptions for the Patriots, who are chasing their fifth Super Bowl championship.
In Atlanta, quarterback Ryan threw for three touchdowns as the Falcons overpowered the Seahawks.
Ryan - the favourite to win the MVP award - has won both his play-off games against the Seahawks but is winless in four post-season starts against other NFL teams.
The New England Patriots reached the AFC title game for a record sixth successive time as Dion Lewis scored touchdowns three different ways in a 34-16 win over the Houston Texans.