He was replaced by Dick LeBeau, the assistant head coach and defensive coordinator, the team said.
The Bengals have been outscored 74-7 this season. They haven't had a winning season since 1990 and have gone 10 years without making the playoffs, the longest current streak in the league.
LeBeau is a former defensive coordinator of the Pittsburgh Steelers. He oversaw the zone-blitz defenses that made the Steelers one of the NFL's top defensive teams in the mid-1990s.
The 63-year-old LeBeau has also served on the coaching staffs of the Philadelphia Eagles and Green Bay Packers. Coslet brought him back to Cincinnati for a second tour of duty.
LeBeau played offensive and defensive back at Ohio State, then played in the NFL for the Detroit Lions from 1959 to 1972 as a cornerback.
Coslet was promoted from offensive coordinator in October, 1996, to succeed the fired Dave Shula when the Bengals were 1-6. The team finished 1996 7-2 under Coslet, giving new hope to Bengals fans deflated by years of losses under Shula.
But it was downhill from there. Under Coslet, the Bengals were 7-9 in 1997, 3-13 in 1998 and 4-12 in 1999.
The Bengals set an NFL record by losing 107 games in the 1990s, 108 if the Jan. 2 loss in Jacksonville, Fla., is included.
The Bengals' 37-0 loss on Sunday in Baltimore was further evidence of their futility on offense. They had lost 13-0 the Sunday before in Jacksonville after a 24-7 loss at home on Sept. 10.
The Bengals and president Mike Brown are under increased pressure to win because Hamilton County taxpayers paid for the $453 million Paul Brown Stadium in which the Bengals started play this season.
Cincinnati's total of seven points in the first three games is the lowest for a three-game stretch since the 1978 team scored three points in three weeks during a 4-12 season. Sunday's loss was the 28th in 35 games under Coslet.
"That was about as thorough a beating as you'll see," Brown said after watching the Bengals rush for just four yards in the Baltimore game.
"There have to be changes," Bengals defensive end John Copeland told the team's Web site. "Each and every player has to change what they are doing.
"It starts with the players. If we don't do it, it can't be done by anybody else," Copeland said.
The Bengals had dipped into the free-agent market during the off-season, signing safety Darryl Williams and defensive linemen Tom Barndt and Vaughn Booker.