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However, the Reds failed to register a shot on target in the opening 45 minutes, with Robert Tesche's drive from distance as close as the hosts came to taking the lead.
Arguably Derby's best opportunity in the first half fell to Johnny Russell when he met Ryan Shotton's cross, but his header was deflected wide.
Antonio had a quiet start to the second half before coming alive by beating Shotton and Russell and unleashing a drive from 25 yards, which Lee Grant needed to be equal to.
The game was halted midway through the second period when a small number of fans invaded the pitch.
Shortly after the game restarted, Forest took the lead when Britt Assombalonga received the ball from Antonio and his shot on the turn from inside the area nestled in the bottom corner.
The away side got back on terms with ten minutes remaining. After Richard Keogh headed the ball against the crossbar, Leon Best hit the ball into the back of the net and wheeled away in celebration, although replays suggest that Shotton got the vital touch in a goalmouth melee.
The result leaves Forest a point clear of second-placed Norwich City in the Championship standings.