Jerry Jones should NOT fire Jason Garrett ... and should instead give him a fat, new contract extension -- so says Emmitt Smith, who tells TMZ Sports the Cowboys coach is great!!!

A lot of fans in Dallas seem to disagree ... JG only has 2 playoff wins in 9 seasons -- but, Emmitt is going to bat for the dude regardless.

The Cowboys legend tells us the job Garrett did bringing the Cowboys back from 3-5 to NFC East Champs this season was awesome ... and he deserves a new deal because of it.

"It takes a skill and a special guy to try to keep players motivated when everyone else is counting you out. And he did that with this team," Smith told us at the EA Sports Madden Bowl.

"Got them in the playoffs, got them to a playoff game, and, obviously, didn't finish, but he has a lot to build upon."

As for all the people clamoring for Tony Romo to take over Garrett's job ... Emmitt says he doesn't know if the ex-QB will be a slam-dunk with instant success on the sideline.