Steve Cooper was determined to make home advantage count for the four-time winners, but Marcus Rashford quickly silenced the Forest faithful with a searing run and finished just in the sixth minute.
A short response midway through half-time put the hosts back on the line before Wout Weghorst netted a timely first goal for the club as half-time approached. Bruno Fernandes secured the game late in the game.
United had started the better side by far and yet lacked the end product to back up their quick play, Antony firing wide with two tame efforts after Rashford’s opener.
In fact, it was from the goalscorer’s gift that Forest first threatened. Morgan Gibbs-White played a fine ball from behind for Sam Surridge to fire home against the run of play. However, VAR brought the move back for a narrow offside.
Gustavo Scarpa and Brennan Johnson threatened for the hosts, now finally an active participant in the encounter, the latter forcing David De Gea to a low stop before a delicious run beat two challenges and fired over the bar.
United appeared to be heading for the break on the back foot, Erik ten Hag furious at Fernandes chopping a long-range shot well wide of the goal. And yet, within moments, they scored again.
Antony’s volley from 18 yards was parried by Wayne Hennessey straight to Weghorst, who managed to maneuver an unorthodox finish into the roof of the net just as the clock hit 45 minutes.
With a foothold at Wembley after just a quarter of the game, United faced some tough questions after emerging for the second half. Christian Eriksen curled an effort over the crossbar after 54 minutes.
Shortly after, Rashford fell clutching his ribs and was quickly taken off after being cut, although he left quite comfortably with his work done for the night at game time.
Ten Hag opted for pace off the bench with Alejandro Garnacho, Anthony Elanga and Facundo Pellistri entering the fray. It was the Uruguayan who caused problems when the ball broke in the 88th minute for Fernandes to volley home from 20 yards and surely book a place in the final.
Forest will try to revive their bid to reach Wembley with the return leg at Old Trafford next Wednesday.