Barcelona was 3-0 in group play leading up to the match, including a 2-1 victory of its own last time it played Celtic.
Now, Celtic is up to seven points in Group G, which is still two behind Barcelona, but gives it an all-important buffer over the two squads below.
Let's take a look at how it all went down.
Score: Celtic 2-1 Barcelona
Victor Wanyama (CEL) 20'
Tony Watt (CEL) 83'
Lionel Messi (BAR) 90'
(20') Victor Wanyama's first-half goal was lovely, as he thumped in a header to put his side ahead 1-0.
(70') Messi puts a beautiful flashing shot on net, but Fraser Forster reaches his massive paw down to the bottom-right corner and blocks it. Best save in a game filled with great ones.
(83') But the highlight of the game had to be Celtic's second goal. After saving a free kick from Lionel Messi, keeper Fraser Forster launched the ball down the field, past Xavi and right onto the foot of Tony Watt. Watt finished and gave Forster an assist.
(90') Messi's goal was classic Messi as well. After a brilliant save from Forster, the diminutive opportunist was first to the ball (as usual) and knocked it in from close range.
Fraser Forster (CEL), A+
The big keeper had the game of his dreams tonight, neutralizing Barcelona's dominant attacks and even tallying the aforementioned assist.
Barcelona outshot Celtic 25-4, netting eight shots on goal to Celtic's two. It controlled possession for 84 percent of the game, too, which means Forster had to be on edge all night long.
If not for its keeper, there's no way Celtic could have pulled off this stunning upset.
Victor Valdes (BAR), F
Valdes isn't asked to do much in the back of Barcelona's defense. With his team controlling 84 percent of the ball, he gets to spend a lot of time off his line, counting blades of grass.
All it asks is that on the rare occasion that he needs to step up, he's ready.
Today, he wasn't. Celtic's only two shots on target both found their way into the net, embarrassing Valdes and leading to an upset defeat. This one's on you, Victor.
Lionel Messi (BAR), B+
Messi looked just as good as he always does, but was unfortunately unable to convert until extra time.
Before his strike into the top of the net, however, Messi created several chances for his teammates and even more for himself. Had the woodwork been kinder to Lionel this afternoon, I could be writing a much different headline right now.
But alas, Messi came up short, which prevents him from securing an A grade against Celtic.