Pep Guardiola's side were 3-0 to the good at half-time thanks to an own goal from Aliaksandr Volodko and further strikes from Pedro Rodriguez and Messi.
The Argentina international grabbed the fourth goal early in the second half with an assured left-footed finish to move level with Ladislau Kubala's total of 194, before David Villa rounded things off as the visitors made light of the sodden conditions.
The win was also Barcelona's second 5-0 win in a row following their weekend success over Atletico Madrid.
As expected Belarusian side BATE found themselves under constant pressure from the off, with Thiago firing a shot straight at keeper Aleksandr Gutor before Messi fizzed a free-kick inches wide of the right-hand post.
The partisan home crowd were on their feet whenever their side entered the Barcelona half, with their only early chance seeing Renan Bressan head over at the near post.
But the opener inevitably arrived after 19 minutes as some typically slick build-up saw Volodko turn the ball into his own net at the far post under pressure from Messi.
The second arrived moments later as Villa's beautifully weighted pass picked out Pedro, who headed beyond the advancing Gutor.
Despite having so much of the ball Barca were almost caught out on the half-hour as Volodko raced on to a through ball, but Carles Puyol produced a fantastic covering tackle.
And normal service was soon resumed as Gutor was forced into a sharp near-post save after Villa had cut in from the left.
The third arrived eight minutes before the interval as Gutor failed to hold a Pedro cross and allowed Messi to steal in and nod home.
Messi then lacerated the BATE defence with a wonderful pass but could not convert when Villa attempted to set him up.
A lovely one-two with Pedro freed the Argentinian early in the second stanza but he fluffed his finish as he closed in on goal.
But he finally moved into joint-second place on the Catalan club's all-time scoring list just before the hour mark as Alves teed him up to fire a left-footed shot high into the roof of the net.
Messi's masterclass continued as another incisive pass gave Eric Abidal a great chance, but the defender was denied by Gutor.
Filipp Rudik had BATE's best chance but lifted the ball over the bar, before Maksim Skavysh failed to collect with a threatening cross. But they would end the night still searching for a first home Champions League goal.
Guardiola was able to rest the likes of Xavi, Pedro and Abidal with the game won as his side cruised through the final quarter of a routine win, with Villa rounding things off in the 90th minute as he slotted low into the net.
BATE: Gutor, Alexander Volodko, Filipenko, Simic, Bordachev, Kontsevoy, Olekhnovich, Baga, Rudik (Aleksiyan 60), Bressan (Kurlovich 81), Kezman (Skavysh 55).
Barcelona: Valdes, Dani Alves, Puyol, Abidal (Adriano 61), Xavi (Fabregas 59), Mascherano, Thiago, Keita, Pedro (Maxwell 69), Messi, Villa.
Goals: Alexander Volodko 20 og, Pedro 22, Messi 38, 55, Villa 90.