Andrew Garfield & Emma Stone -- Caught Red-Handed ... Speeding

Spider-Man is only allowed to use his superhuman speed to fight crime, not when he's behind the wheel ... so when Andrew Garfield was speeding through Malibu with Emma Stone yesterday ... he got busted.

"The Amazing Spider-Man" co-stars (who are a couple in real life) got a surprise visit from a cargo-shorts-wearing LA County Sheriff (above) ... when Garfield was pulled over for having a lead foot.

We're told he was cited for speeding and then sent on his merry way. It's unclear how fast he was going or if he was on a mission to rescue someone.