The Catalans' passing was as tight and crisp as ever as goals from 19-year-old Sergi Roberto, 20-year old Martin Montoya and two from Pedro, at 24 the third oldest player in the starting line-up, earned them a convincing win.
With his side already guaranteed top spot in Group H, and with one eye on Saturday's trip to the Bernabeu to face Primera Division leaders Real Madrid, coach Pep Guardiola rested virtually his entire first XI.
But if BATE hoped the absence of the likes Lionel Messi, Xavi, Andres Iniesta and David Villa would give them a chance of springing an upset and avoiding last place in the group, they were sorely mistaken.
The names may have been different, but the speed of movement and confidence on the ball was very familiar as Barcelona dominated from the first whistle.
Brazil-born Spaniard Rafinha almost put the hosts ahead in the second minute when he wriggled free in the area, but his shot was blocked by goalkeeper Aleksandr Gutor.
For all their high-tempo passing, Barcelona were struggling to find a way through the BATE backline.
Sergi Roberto had the clearest chance in the 34th minute when Martin Montoya slid a low ball from the right across the face of goal which his team-mate, sliding in at the far post, directed just wide.
The 19-year-old scored just a minute later, though, side-footing the ball calmly first time into the bottom corner after it broke to him just inside the area.
The lively midfielder had another effort before the break but his snap-shot was straight at Gutor.
The one-way traffic continued in the second half as Sergi Roberto went clear only to be denied by good save from Gutor.
Pedro's clever lob was then clawed away by the keeper, who was beaten again in the 60th minute.
Montoya, up from right-back, ran on to Isaac Cuenca's perfectly-weighted through-ball and, getting to the ball just ahead of Gutor, placed a shot high into the net.
It was 3-0 three minutes later when Cuenca cut the ball back for Pedro - whose status as a regular in the first-team squad the youngsters are looking to emulate - to score with a classy backheel through the keeper's legs at the near post.
Marti Riverola crashed a shot just wide as Barcelona kept on pressing and they won a penalty two minutes from time.
Cuenca was tripped in the area by Alexander Volodko and Pedro sent Gutor the wrong way to bring up his 50th goal for Barca.