France striker Giroud headed in Emerson Palmieri's cross in the 52nd minute to decide a tentative contest and break his club drought dating back to May.
BATE, who hit the woodwork three times, would have been deserving of a point, but will now seek to revive their hopes in their next meeting with Vidi, who edged PAOK 1-0.
That result means the Blues, having racked up a fifth successive competitive victory, must wait until the Greek side's visit later this month to confirm top spot in Group L.
Two goals down inside eight minutes at Stamford Bridge a fortnight ago, BATE were unfortunate not to be ahead early on home soil as Dmitri Baga crashed a long-range shot against the post.
Chelsea soon settled into a dominant share of possession without ever looking like making the breakthrough before half-time.
Giroud had fleetingly threatened with one header before the break and it was in similar circumstances that he opened the scoring, convincingly meeting Emerson's cross at the near post.
Only another moment of misfortune prevented BATE from responding quickly, with Nikolai Signevich's close-range effort coming back off the underside of the crossbar, before an unmarked Aleksey Rios skied an even more promising opening.
Eden Hazard was withdrawn just after the hour and with him went the last of Chelsea's minimal attacking verve as it settled for an uninspiring, albeit important, 1-0 victory after the upright denied substitute Evgeni Berezkin.