A B737 CAPT; ADMITTING TO FATIGUE; ANNOUNCED THE SHUTDOWN OF ONE ENG AT THE GATE; BUT ACTUALLY SHUT DOWN THE OTHER. THE RAMP PERSONNEL WERE CONFUSED; THE CAPT DID NOT COMMUNICATE IN A TIMELY FASHION; AND THEN A BAGGAGE HANDLER DROVE UP BEHIND #2 NEARLY CAUSING INJURY AND DAMAGE.

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DURING A STOPOVER AT MLI; I HAD INFORMED THE STATION THAT I WOULD SHUT DOWN #2 ENG ONLY AS OUR APU BLEED AIR WAS DEFERRED. I WAS RATHER FATIGUED AND ACCIDENTALLY SHUT DOWN THE #1 ENG UPON REACHING THE GATE. THE MECH CAME ON BOARD AND ASKED ME WHY #2 ENG WAS STILL RUNNING. I ASSUMED THAT ALL THE GND PERSONNEL WERE INFORMED THAT #2 ENG WAS STILL RUNNING AS THE MECH SAID HE INFORMED SOME OF THE BAGGAGE HANDLERS TO STAY CLR. WHILE WE WERE TRYING TO DECIDE WHETHER TO SHUT DOWN #2 ENG AND TRY TO FIND AN AIR CART OR XBLEED #1 ENG THEN SHUT DOWN #2 ENG; A BAGGAGE CART APPARENTLY DROVE BEHIND THE RUNNING #2 ENG. ACCORDING TO THE MECH; NO ONE WAS INJURED; BUT OBVIOUSLY IT COULD HAVE LED TO AN INJURY. EVENTUALLY WE XBLED THE #1 ENG AND SHUT DOWN #2 ENG TO ALLOW THE BAGGAGE TO BE LOADED. I BELIEVE BEING SOMEWHAT TIRED AND TRYING TO HURRY OUR GND TIME CONTRIBUTED TO MY ERROR; BUT I HAVE TO LAY MOST OF THE BLAME ON MYSELF; AS MY HEAD WAS UP AND LOCKED WHEN I SHUT DOWN THE WRONG ENG. I SHOULDN'T HAVE ASSUMED THAT THE GND PERSONNEL KNEW THE MOTOR WAS STILL RUNNING. I ALSO FEEL THAT IF I'D HAVE USED BETTER CRM BY INFORMING MY FO THAT WE'D BE SHUTTING DOWN #2 ENG (IN ADVANCE) HE WOULD HAVE BEEN MORE IN THE LOOP AND NOTED MY ERROR. FINALLY; IT IS POSSIBLE THAT THE COMPANY MIGHT CONSIDER A SUPPLEMENTARY TYPE CHKLIST; AS THIS PROC IS SOMEWHAT NONSTANDARD.