The Academy Award nominee and UFC superstar opened up on working together on set during a recent episode of "Armchair Expert" with Dax Shepard ... and while they both praised each other's professionalism, there was a bit of bad blood involved.

Gyllenhaal -- who plays former MMA fighter Elwood Dalton in the flick -- explained he was shooting an intense showdown with Conor's character, Knox ... and the scene involved a ton of breakaway glass.

As it turns out, it didn't matter if it was real or fake ... 'cause when Gyllenhaal put his hand down on the bar in the middle of the take, a piece went right through his mitt.

But, there was no quit in the lead actor -- he said he trucked through the shot and finished the scene because they had already run through it several times and he knew this take was a good one.

Once the director called "cut" -- shoutout irony -- Gyllenhaal said he looked down at his hand and noticed his whole arm had swelled up ... and he later found out it was a staph infection.

Of course, staph can be a real pain in the ass ... but it can also be deadly in some cases if it goes untreated.

Luckily, Jakey G is still kickin' ... and he said that was really the only injury he had while filming the Prime Video flick.

Conor ain't the only big-name non-actor in the project -- Post Malone also showed off his acting chops ... and based on BTS pics, the musician got pretty bloody, too.