After the restart, Szczęsny produced an excellent save to deny Arda Güler following a quick counterattack from Vinícius.
Liverpool ended their eight-game losing run with a dominant 5–1 win on an away trip against Eintracht Frankfurt.
Real Madrid hosted French side Olympique Marseille, with Xabi Alonso avoiding a debut defeat thanks to Kylian Mbappé.
The result means Arsenal have progressed in 19 of 21 UEFA knockout ties after winning the first leg at home.
It was a case of what might have been for Chelsea, whose winless run extends to seven matches across all competitions.
Carlo Ancelotti now becomes the first manager to win league titles in each of Europe’s ‘big five leagues.
