It was a fourth Group L victory from four games for Maurizio Sarri’s team who have confirmed their place in the last 32 of the competition with two games still to go.
However, BATE, who won their 13th consecutive Belarusian league title at the weekend, hit the woodwork twice and were a little unfortunate not to at least draw the match.
The home team went close to breaking the deadlock in the 12th minute when former Arsenal midfielder Alex Hleb played in Dimitri Baga whose superb 25-yard shot hit the post.
Chelsea struggled to create many clear-cut openings in the first half although Giroud did head Eden Hazard’s corner wide but they improved after the break and moved ahead in the 52nd minute.
Emerson Palmieri’s cross found Giroud whose header should have been dealt with by BATE goalkeeper Denis Scherbitski who got a touch to the ball but could not keep it out.
The Belarusian champions went close to grabbing an equaliser six minutes later when Nikolai Signevich hit the woodwork while an unmarked Aleksey Rios contrived to miss the target from 12 yards out when it seemed easier to score.
Ross Barkley’s 25-yard shot was tipped over the bar by Scherbitski before Hazard was substituted just past the hour mark.
Barkley and Giroud went close to doubling Chelsea’s lead in the closing stages as a dull encounter petered out.
However, Sarri’s side had already done enough to confirm their place in the knockout stages of the Europa League and they can now focus on domestic matters for the next three months.
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