© PA Photos
Despite rarely threatening the Barcelona defence, it was Celtic who took the lead in the 21st minute when Charlie Mulgrew delivered a corner towards the back post to allow Victor Wanyama to head powerfully past Victor Valdes.
The visitors did have opportunities to equalise before the break but a superb save from Forster denied Lionel Messi before Sanchez clipped the post with a looping header on the stroke of half-time.
Messi continued to pose the biggest threat to Celtic's lead after the interval and tested Forster's reflexes again with a curled effort from the edge of the box.
Forster came to Celtic's rescue on the hour mark when he twice stretched himself to block close range efforts from Sanchez.
Celtic could have extended their lead as Mulgrew was allowed to find space inside the area following a defensive mistake but Marc Bartra recovered well to block the resulting shot.
Messi's night of frustration continued when, after exchanging passes with Andres Iniesta, he was once again denied by the brilliance of Foster in the home side's goal.
Despite being forced onto the back foot for most of the second half, Celtic launched a counter attack in the final stages and substitute Tony watt was able to finish calmly past Valdes to double the home side's lead.
Messi finally beat Forster in stoppage time with a close-range finish but Celtic held on to complete a memorable victory.