Goals from Charlie Mulgrew and Anthony Stokes were followed by a Kris Commons double within a 20-minute period in the second half as the visitors cruised to victory to go 13 points clear of Aberdeen at the top of the table.
After the game, Buddies boss Danny Lennon claimed a continuation of Celtic's run was not "beyond them".
However, the Northern Irishman, whose side fly out to Turkey this morning for a winter break, said: "There is a long, long way to go.
"To go to St Mirren, having seen what they did to Dundee United 10 days ago (won 4-1), speaks volumes for the intensity and concentration of the players.
"They was a real desire about them.
"We wanted to go into the break unbeaten and we got the goals, we got the clean sheet and got the three points.
"To go unbeaten the whole season is almost impossible, although we made big inroads into that.
"All I want to do is stay unbeaten as long as we can, that is the real carrot for the players."
The Scottish champions are scheduled to play two games in Turkey in the Antalya Cup, a tournament which also involves Galatasaray, Trabzonspor and Dutch champions Ajax.