The hosts reached their first cup semi-final since 1981 and maintained the dream of ending their 33-year trophy drought.
At the same time, Arsene Wenger was left staring at the wreckage of a wretched week which may beg the question of whether his grand plan is that grand after all.
Tevez opened the scoring five minutes after the break, cutting inside from the left before lashing home a curling shot into the top corner.
Wright-Phillips lashed home a brilliant second on 69 minutes before Weiss tapped home his first City goal a minute from time.
City now face derby rivals Manchester United in a two-legged semi-final, with the first tie at Eastlands to be played during the week commencing January 4.