Marcus Tudgay scored the first goal of the Cotterill era, providing the finishing touch to a flowing Forest move that epitomised their football in the first half.
Lewis McGugan capped a fine individual performance with a superb second goal shortly after half-time to inflict a first league defeat of the season on Middlesbrough and lift Forest out of the Championship relegation zone.
Cotterill, officially unveiled as Steve McClaren's successor on Monday after a compensation package was agreed with Portsmouth on Friday, made two changes to the team Rob Kelly picked at Coventry at the weekend.
Former Boro boy Jonathan Greening missed out against his old club and dropped to the bench along with Matt Derbyshire. Joel Lynch and Radoslaw Majewski came into the starting XI.
Middlesbrough made four changes. Matthew Bates and Rhys Williams missed out with knocks, while Julio Arca and Scott McDonald started on the bench. Seb Hines, Faris Haroun, Justin Hoyte and Stephen McManus were recalled.
Forest started confidently, passing the ball about and keeping possession but without threatening the Middlesbrough goal.
Chances were scarce in the first half. Tudgay dispossessed Hines on the edge of the box in the sixth minute but rushed and shot wide when he had more time.
McGugan's long-range free-kick struck Ishmael Miller 12 yards out and skidded past the post after 21 minutes.
When the opening goal arrived 10 minutes before the break, it was something of a surprise. Forest's football suddenly found some penetration when Miller threaded a pass between Hines and Joe Bennett to release Chris Gunter.
The Wales international whipped a low cross into the six-yard box where Tudgay beat two covering defenders to the ball to tap home.
Forest almost doubled their lead before the break when McGugan's corner fell to Luke Chambers at the front post but the captain's goalbound volley struck Miller in front of the goal and went over the crossbar.
Middlesbrough should have equalised at the start of the second half but Nicky Bailey headed Barry Robson's inswinging free-kick wide at the far post.
McGugan almost made Boro pay when he dispossessed Marvin Emnes in the centre circle and embarked on a driving run, evading two challenges en route to the penalty area before shooting wide.
However, McGugan found the target in the 55th minute. Miller and Majewski had shots blocked inside the area before the ball broke to McGugan on the edge of the box.
The midfielder danced past a defender and unleashed a right-foot shot into the bottom corner.
McGugan continued to pull the strings and another of his deliveries found the head of Wes Morgan but the big defender glanced his header wide.
At the other end, Lee Camp was called into a rare piece of action when he tipped a shot from Hoyte round the near post with 15 minutes remaining.