Frank Lampard's side were rocked when Kortney Hause put Villa ahead against the run of play in the first half.
But Christian Pulisic came off the bench to equalise after the break before Giroud bagged his fourth club goal of the season two minutes later.
Chelsea's quick-fire blitz moved the fourth placed west Londoners five points clear of Manchester United in fifth in the race to qualify for next season's Champions League.
A first away league win of 2020 was the ideal way for Chelsea to return to action in their first match since the Premier League was suspended in March due to the coronavirus.