Rosenior’s side had beaten second-tier Charlton 5-1 in his debut in the FA Cup third round last weekend.
But Arsenal ensured his first game on the Stamford Bridge bench was significantly less enjoyable.
Ben White put the Premier League leaders ahead in the first half and Viktor Gyokeres punished a blunder by Chelsea goalkeeper Robert Sanchez to score their second after the interval.
Alejandro Garnacho came off the bench to pull one back for Chelsea before Martin Zubimendi grabbed Arsenal’s third goal.
Garnacho gave Chelsea a glimmer of hope with his second goal in the closing stages.
But Arsenal will go into the second leg at Emirates Stadium on February 3 as firm favourites to reach the Wembley final in March.
Manchester City won 2-0 at Newcastle in the first leg of the other semi-final on Tuesday.
Arsenal are unbeaten in their last 10 matches in all competitions as they try to win their first trophy since the 2020 FA Cup.
Gunners boss Mikel Arteta had claimed his players were motivated by their 4-0 aggregate defeat against Newcastle in the League Cup semi-finals last season.
They also lost in the semi-finals of the 2025 Champions League, the 2022 League Cup and the 2021 Europa League.
Top of the Premier League and Champions League, and through to the FA Cup fourth round, Arsenal may never have a better chance to end their silverware drought.
Rosenior, sacked by Hull in 2024, was hired by Chelsea last week to replace Enzo Maresca after earning plaudits for leading French club Strasbourg to a seventh-place finish last season.
The 41-year-old’s introduction to Stamford Bridge was hampered by the absence of Cole Palmer, Moises Caicedo, Reece James, Liam Delap, Jamie Gittens and Malo Gusto due to a combination of injuries, illness and suspension. (AFP)
