Early chances were exchanged in a quiet opening with Ilkay Gundogan slipping a shot wide after Mohamed Salisu’s effort before Duje Caleta-Car forced Stefan Ortega into a fine parry to deny his bouncing volley.
Southampton were booed off in their last game at St Mary’s but looked a far more motivated team from the off and took the lead after a scrappy period of play on 23 minutes.
Lyanco stole possession to stride forward and slot a fine cross for Sekou Mara to finish, marking his first goal for the club.
It was 2-0 only five minutes later when Moussa Djenepo was allowed to run through the absent City midfield and spot Ortega off his line, producing a brilliant chip from 25 yards out.
City held plenty of possession in reply, clocking 72 per cent of the ball at the break, but with little to no end product to speak of.
Kevin De Bruyne came on in one of three half-time substitutions from Guardiola, who had won all 15 of his domestic cup quarter-finals as a manager before tonight. Instantly, he found the previously anonymous Julian Alvarez for a shot across goal.
It was only ten minutes later when Erling Haaland was called upon from the bench as Southampton dropped to a five-man defence.
Yet the visitors were surprisingly low energy and entered the final 20 minutes still without a shot on target, Gavin Bazunu enjoying a fine night in the Saints goal with superb command of his box.
In truth, a great siege on the hosts’ goal was not forthcoming as a vulnerable City faded out of contention for this year’s Carabao Cup.