After a 3-0 victory in last week's last 16, first leg at Stamford Bridge, 2013 winners Chelsea were even more dominant in Kiev despite manager Maurizio Sarri ringing the changes, thumping the Ukrainians 5-0.
The Premier League giants are bidding for a first trophy under the Italian after losing last month's English League Cup final to Manchester City, and hoping to secure qualification for next season's Champions League.
Giroud, who is yet to start in the Premier League in 2019 after the signing of Gonzalo Higuain, netted a first-half double, before Marcos Alonso slid home a third on the stroke of half-time.
Frenchman Giroud completed his first Chelsea hat-trick by heading home Willian's free-kick just before the hour mark and is now the leading scorer in this year's competition with nine goals.
Teenage winger Callum Hudson-Odoi continued his own fine Europa League form, slotting in his fourth goal of the tournament after racing clear with 12 minutes remaining.
Elsewhere, Napoli wrapped up a 4-3 aggregate victory over last season's semi-finalists Salzburg despite a 3-1 second-leg loss in Austria.
Arkadiusz Milik scored a crucial away goal in the 14th minute to all but end the tie, leaving Salzburg needing five unanswered goals to progress.
Munas Dabbur and Fredrik Gulbrandsen struck to give the hosts a glimmer of hope, but Christoph Leitgeb's injury-time third goal was only enough to secure a consolation win on the night.
Russian outfit Krasnodar suffered heartbreak in the other early game, as Goncalo Guedes scored a dramatic injury-time equaliser to send Valencia through 3-2 on aggregate after a 1-1 second-leg draw.
The 19-year-old Magomed-Shapi Suleymanov's 85th-minute effort looked set to dump out the Spaniards on away goals, but Portugal international Guedes came off the bench to send Valencia through.
Marcelino's men have recovered well from a slow start to the season, having also reached the Copa del Rey final and stepped up their bid for a top-four place in La Liga.