Gareth Taylor’s side will meet Everton at Wembley in 1 November’s showpiece, live on BBC One, after the Toffees beat Birmingham City 3-0 on Wednesday.
Steph Houghton’s curling free-kick opened the scoring before Jordan Nobbs levelled with a fine long-range strike.
But United States midfielder Sam Mewis quickly restored City’s lead and they remained on top in the second half.
World Cup-winner Mewis’ first goal in English football sent City through to the club’s third Women’s FA Cup final, all of which have come since 2017.
Record 14-time winners Arsenal had been bidding to reach their 17th final but were not able to reproduce the form they had shown in September, when they scored 19 times in three games in all competitions.
It is time for Manchester City to prove that they are capable of retaining their position in the women’s FA cup.