Everton are without Chelsea loanee Kurt Zouma, who is ineligible to play against his parent club, so summer signing Yerry Mina will hope to start his first league game for the Toffees.
BATE were denied by the woodwork three times, including once in stoppage time as the hosts went within inches of rescuing a result in frosty conditions.
Chelsea tops Group L with a maximum 12 points.
"The first two away we played with 10 players and nearly won". I think we didn't play very well, I didn't like the first half because we moved the ball only horizontally and slowly, so it was hard to be risky. "We felt that for him it's better to play, not for 90 minutes, but to play after two weeks of not playing", the Italian coach explained.
Giroud had gone 795 minutes without finding the net for Chelsea before nodding in Emerson's inviting delivery from the left flank in the 52nd minute, and speaking to BT Sport after the match he expressed his relief at breaking his duck. "Little Bernard has been brilliant so we've got very good players".
"I think Sarri's looking at that and they Man City (are looking good for the title), he's looking and thinking "we've got a chance of winning the Europa League, a big chance of winning it".
Giroud's goal was a rare Chelsea effort on target.
"I am pleased for him".
"At the beginning he was in trouble", the 59-year-old former Napoli boss said. "For his confidence it is very important".
"But you always need to keep working hard in training and keep believing, keep the faith". "That's what I did tonight".