Leyton Orient saw their winless run in League One extend to eight matches after Brandon Cooper suffered a first-half dismissal against Derby.
Joe Pigott had an early effort blocked at Brisbane Road, after being teed up by Ruel Sotiriou from Theo Archibald's cross.
And Pigott then played Archibald in moments later, but the Scot misjudged his effort from inside the box.
Sol Brynn grabbed Kane Wilson's effort as Derby had their first sight of goal on seven minutes, with Rams captain Conor Hourihane booked for bringing down Rob Hunt.
Louie Sibley volleyed over for the visitors on 13 minutes, before Sotiriou forced Joe Wildsmith into a save with an angled attempt.
Curtis Nelson cleared the danger after more good work from Sotiriou almost created a chance for Pigott midway through the half, with Wildsmith saving from Jordan Brown after Tom James and George Moncur had combined.
Brynn made a superb save to keep out Joe Ward's low free-kick on 27 minutes, but Derby broke the deadlock seven minutes later when Sibley struck from outside the box.
O's had a let-off when James Collins fired wide with the goal at his mercy five minutes before the break but the hosts were reduced to 10 men when Cooper was sent off for a challenge on Collins.
Moncur made way for Omar Beckles as a result of the red card but O's conceded a second within two minutes of the restart as Nathaniel Mendez-Laing netted.
Beckles found the net from a James free-kick only to be denied by an offside flag, before Pigott made way for Darren Pratley.
And O's made a double change just past the hour as Archibald and Sotiriou were replaced by Shaq Forde and Dan Agyei.
Brynn made a good save to deny Mendez-Laing a third Derby goal after he broke through the O's defence on 71 minutes, before Brown saw an effort deflected behind for the hosts and Hunt flashed the ball across the six-yard box but just beyond Agyei and Pratley on 75 minutes.
However, Tom Barkhuizen ended any faint hopes of a comeback from the 10 men when netting Derby's third goal of the game 11 minutes from time, although Agyei was inches away from a reply when hitting a post moments later.
Leyton Orient: Brynn, James, Happe, Brown, Pigott (Pratley 53), Sotiriou (Agyei 62), Archibald (Forde 62), Cooper, Moncur (Beckles 45), El Mizouni, Hunt.
Unused subs: Howes, Sweeney, Galbraith.
Attendance: 8,499 (including 1,196 Derby fans).
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