The draw against Salzburg left Graham Potter's side with an uphill task to reach the knockout stages of the competition.
In his competition debut, the former Seagulls boss chose to play an advanced wing-back but his gamble paid off when the forward curled into the bottom corner.
It was a much better performance than the one they gave against Dinamo Zagreb in their first game of the season.
The Austrian side got an equalizing goal on 75 minutes after Thiago Silva missed a tackle.
The risks of Potter's approach were highlighted by that goal. The hosts had a chance to win when James fired over from a free-kick, but he missed.
Following AC Milan's victory over Zagreb, the Blues are bottom of the group after two games.
After a week in which he called a "whirlwind", Potter got his first taste of Europe's premier club competition, having never been before.
He only managed for three years in the premier league with the Seagulls. Although it was a positive display from his side and they wasted several good chances late on, he will now realise he has to quickly turn things around in Europe.
The 47-year-old, who watched in a black suit, quickly established his own stamp on the team by dropping three players from the side.
Silva and Cucurella made up a back three with Cesar Azpilicueta, but the biggest surprise was seeing sterling at left wing-back.
The forward was stationed up the pitch for most of the game and wasted two good chances in the first half.
Within a minute of each other, the two teams were able to open the scoring. Benjamin Sesko had a curling effort tipped around the post by Kepa Arrizabalaga after sterling gave the ball away after Mason Mount sliced a shot inches wide of the post.
Three minutes after the break, the Englishman showed why he was positioned so far up the pitch.
James started the move on the right flank with a powerful run and fed Mount, whose cross was mishandled by Pierre-Emerick. The inside of the post for this fourth of the season was fortunately found by sterling.
They looked like they would add to their lead at that point.
The desire to play in Salzburg's half backfired when the two players were dispossessed near the halfway line.
He seemed to be closing down Adamu after the ball was played wide.
The normally reliable Brazilian missed the tackle, with Okafor adding to the goal he scored against AC Milan last week.
There were a lot of chances for the Blues to take the lead again, but Potter made five replacements in order to get a goal.
The Austrians were able to hold on after the two wasted money.
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