The win elevated the Steelers from winless to within a game of first place in the AFC North at 1-3. The Bengals fell to 0-4 under first-year coach Zac Taylor.
Rudolph, in his second start since future Hall of Fame quarterback Ben Roethlisberger sustained a season-ending elbow injury, completed 24 of 28 passes. He threw TD strikes to James Conner, who amassed 125 total yards, and Diontae Johnson.
Pittsburgh's Jaylen Samuels rushed for a touchdown.
An early Randy Bullock field goal accounted for the Bengals' scoring.
Cincinnati quarterback Andy Dalton, still without top receiver A.J. Green (ankle), finished 21 of 37 for 171 passing yards with an interception and was sacked eight times -- with Cam Heyward credited with 2 1/2 sacks.
Cincinnati capitalized on a Steelers turnover in the first quarter. Rudolph completed a pass to Johnson, but Nick Vigil forced a fumble and Jessie Bates III recovered for the Bengals at the Pittsburgh 15-yard line.
That led to Bullock's 28-yard field goal for a 3-0 lead.
In the second quarter, Pittsburgh drove 46 yards in five plays, culminating in Rudolph's 21-yard scoring pass to Conner on a sprint-out to flip the lead to 7-3.
The Bengals were driving well later in the second quarter and reached the Pittsburgh 18 before Dalton dropped back and had the ball chopped away by Bud Dupree. The fumble was recovered at the 29 by the Steelers' T.J. Watt.
Pittsburgh drove the other way and upped its lead to 10-3 on Chris Boswell's 29-yard field goal with 1:01 left in the half.
Rudolph was 17 of 18 for 133 yards and one touchdown in the first half, and he picked up where he left off after halftime. He teamed with Conner and Samuels to march the Steelers downfield, and Samuels scooted untouched 2 yards out of the wildcat for a touchdown and a 17-3 Steelers lead.
Just 1:12 later, following a Cincinnati punt, Rudolph hit Johnson on a 43-yard scoring play to make it 24-3.
Boswell's 49-yard field goal with 5:51 left in the game made it 27-3.
--Field Level Media