The Bengals' win sets up a repeat of last year's AFC Championship clash with the Kansas City Chiefs while the 49ers will face the Philadelphia Eagles for a place in the NFL's Super Bowl.
While the Bengals will again be slight underdogs against Patrick Mahomes and company, they showed all their qualities of tough, no-nonsense football, with their offensive line giving outstanding protection to quarterback Joe Burrow.
Burrow completed 23 of 36 passes, throwing for 242 yards and two touchdowns while running-back Joe Mixon put up 105 yards and a touchdown on 20 carries.
"It was a complete game from everybody, offence, defence, special teams, domination from start to finish, that is what we expected," Burrow told CBS television.
The Bengals set the tone from the opening series with Burrow leading his team on a six-play, 79-yard drive completed with a 28-yard touchdown pass to Ja'marr Chase.
Cincinnati soon had a 14-0 first-quarter lead with Burrow finding an open Hayden Hurst with a 15-yard TD pass.
Injured Bills safety Damar Hamlin, who suffered a cardiac arrest in the abandoned regular season game against the Bengals earlier this month, was watching the game from a suite and received a standing ovation when he was introduced to the crowd.
But despite the home-field advantage, the Bills struggled to get their offence moving until quarterback Josh Allen got them on the scoreboard with a one-yard rush at the end of a 15-play drive in the second quarter.
The Bengals thought they had a third touchdown just before half-time with a superb Burrow pass to Chase at the back of the end-zone but the catch was ruled incomplete after review and Cincinnati had to settle for a field goal which sent them in 17-7 up at half-time.
A Bills field goal brought them within a score of levelling the game but the Bengals were playing with a smart, disciplined approach and they extended their lead when the tireless Mixon finished off a 12-play drive with a one-yard rush.
See the summary from Buffalo Bills v Cincinnati Bengals.
Cowboys wait continues
The Cowboys' 27-year wait for a return to the Super Bowl continues after they once again failed to get past the divisional round.
Dallas have lost on each of the last seven occasions they have reached the divisional round. In a gruelling game dominated by the defences, they were hampered by losing their lead running-back Tony Pollard with an ankle injury in the second quarter.
After San Francisco opened the scoring with a field goal, Dallas responded with a second-quarter four-yard touchdown pass from Dak Prescott to Dalton Schultz.
But troubled kicker Brett Maher missed the extra-point conversion - the sixth miss in his last seven kicks - and two interceptions from Prescott before the half didn't help.
Robbie Gould had no such problems, converting from 47-yards and 50-yards before half-time to give the 49ers a 9-6 lead at the break.
Maher's relief was evident after he was successful with his field goal attempt from 25 yards in the third quarter.
But San Francisco, led by rookie quarterback Brock Purdy, then produced the best drive of the game with George Kittle juggling the ball to complete a crucial 29-yard catch before the series ended with Christian McCaffrey's two-yard burst into the end-zone.
Down seven points, Dallas came up against an impressive San Francisco defence, living up to their ranking as the league's number one.
Maher struck a 43-yard effort between the sticks but with Gould responding and the 49ers not offering the Cowboys any gifts, Dallas were left with 45 seconds to try and conjure up a miracle that didn't materialise.
Purdy, a seventh-round draft pick, didn't throw a touchdown but nor did he throw an interception as he threw for 214 yards completing 19 of 29 passes and notched up his seventh straight win since being thrust into the starting role.
"He's playing at a high level," Kittle said of his quarterback. "Getting our best players the ball. He's awesome and confident in the huddle. He's just doing a great job."
