The France international was yet to find the net under Maurizio Sarri's tutelage in what is his first full campaign at Stamford Bridge.
But seven minutes after half-time in Belarus, Giroud broke the deadlock with a near-post header from Emerson Palmeri's left-wing cross.
Goalkeeper Denis Scherbitski got two hands to the effort but was unable to prevent the 32-year-old from ending a 794-minute wait for a goal, which was enough to give Chelsea a 1-0 win.
The drought dates back to the win over Liverpool last May, when the World Cup winner scored the only goal in a 1-0 success in Antonio Conte's penultimate Premier League home game in charge.
Oliver Giroud’s goal vs. BATE Borisov is his first club goal for:
794 minutes of playing time
A crucial opener in Belarus. pic.twitter.com/Ho762uNqIH
— Squawka Football (@Squawka) November 8, 2018
Giroud broke a run of 1000 minutes for without a goal for club and country with a stunning volley for France in their UEFA Nations League win over Netherlands, earlier in the campaign.
The Belarusians will be sick of the sight of Giroud, having seen him score twice against them in last season's competition for Arsenal.
Manager Sarri had been calm over Giroud's continued failure in front of goal and insisted the streak was "not a problem".
He said: “You know the characteristics of Giroud: Giroud usually is not used to scoring a lot of goals in a season.
"But he’s always very, very useful for the team, for his team-mates. So Giroud is not a problem for us."