Celtic had travelled to Barcelona on the back of a 5-1 win at home to bitter rivals, Glasgow Rangers, but the gulf in class between Spanish and Scottish football was being made clear, although it wasn't until the 50th minute when Neymar scored a spectacular free kick.
Iniesta, who had replaced Ivan Rakitic at the break, added the fourth in the 59th minute with a low shot and a minute later Messi completed his hat-trick after Suarez had beaten the offside trap.
The Uruguayan scored the sixth with 15 minutes remaining after controlling a Neymar pass on his chest and netted his second and Barca's seventh of the night two minutes from time from a Messi pass after the Argentinean had seen a shot tipped wide for a corner.