B733 FLT CREW MAKES WRONG RWY APCH AND LNDG DURING A NIGHT OP AT MDW; IL.

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NEITHER OF US HAD SLEPT WELL THE NIGHT BEFORE. HE HAD A SORE NECK AND MY ROOM HAD BEEN NEXT TO THE MAID'S UTILITY ROOM WHERE THE NOISE STARTED AT XA30. WE WERE GLAD THAT THIS WAS THE LAST AND EASIEST DAY OF OUR TRIP. WE WERE SCHEDULED FOR 4 LEGS AND 8 HRS OF DUTY. THAT ALL CHANGED WHEN WE ARRIVED AT THE ARPT AND OPS INFORMED US THAT OUR FLT WAS RUNNING 3-4 HRS LATE. THERE WERE MULTIPLE LINES OF TSTMS MOVING THROUGH ZZZ. WE WERE FINALLY RELEASED FROM GATE HOLD 6 HRS LATER AND DEPARTED FOR ZZZ. THERE WERE STILL TSTMS ON THE ARR AND WE WERE THE PATHFINDERS FOR THE ARRS FROM THE S. I WAS HOPING THAT OUR FLT TO OUR NEXT CITY AND BACK TO ZZZ WOULD BE STUBBED SO THAT WE COULD GET BACK ON SCHEDULE TO MDW BUT; NO SUCH LUCK. WE FLEW THE NEXT LEG ALMOST FULL BOTH WAYS. FLYING BACK TO ZZZ WE BOTH REALIZED WE WERE TIRED; BUT THERE WAS A PLANE FULL OF PEOPLE THAT NEEDED US TO GET THEM TO MDW. ON OUR FLT TO MDW; I MENTIONED TO MY FO THAT HE HAD THE COCKPIT PRETTY COLD. HE SAID HE THOUGHT THAT WOULD HELP KEEP US AWAKE AND ALERT. WE GOT A DIRECT CLRNC TO MDW AND A XING RESTR TO CROSS 20 MI E OF MDW AT 10000 FT. THIS SEEMED A LITTLE STRANGE; BUT HEY; IT WAS LATE AT NIGHT AND THERE WASN'T MUCH TFC. MDW ATIS SHOWED GUSTY WINDS AND THE ILS TO RWY 4R CIRCLE TO RWY 13C. I BRIEFED THE APCH; BUT WE BOTH AGREED THAT WE WOULD PROBABLY GET THE VISUAL TO RWY 13C AND SET THE ILS IN OUR RADIOS AND SET THE INBOUND COURSE. I WAS STILL USING LNAV TO THE FIX WHEN WE WERE HANDED OFF TO APCH AND THEY CLRED US TO 6000 FT; AT ABOUT 10 MI NE OF MDW. WE CALLED THE ARPT AND WERE CLRED FOR THE VISUAL TO RWY 13C. AT 5 MI N AND DSNDING THROUGH 5000 FT; WE WERE HANDED OFF TO THE TWR AND THEY CLRED US TO LAND ON RWY 13C. WE WERE STILL A LITTLE HIGH AND I DIDN'T WANT TO GO TOO FAR TOWARD OHARE AIRSPACE; SO I DECIDED TO CONFIGURE ON SPD TO FLAPS 40 DEGS AND KEEP A 4 MI PATTERN. I CONTINUED TO DSND ON THE BASE AND JUST PRIOR TO TURNING FINAL; I NOTICED MY HSI SELECTOR WAS STILL ON NAV; SO I FLIPPED IT UP TO MONITOR THE ILS. I ALSO REALIZED WE HADN'T RUN THE 'BEFORE LNDG' CHKLIST; SO WE COMPLETED IT. AS I TURNED ON FINAL; I CHKED THAT WE WERE ON GS AND SINCE I WAS STILL A LITTLE N OF THE EXTENDED CTRLINE; THE LOC WAS NOT CTRED. I ROLLED OUT ON FINAL; MADE MY 1000 FT CALLS. (WE WERE CONFIGURED; ON SPD; AND GS. I TRANSITIONED TO THE VASI AND MADE A SMOOTH TOUCHDOWN ON THE 1000 FT MARKER.) AFTER MODERATE USE OF BRAKES AND THRUST REVERSE; WE WERE CLRED BY TWR TO EXIT THE RWY AND TAXI TO THE GATE. THE FO SAID THAT OPS MIGHT HAVE US WAIT OUT BECAUSE OUR GATE WAS OCCUPIED. I THOUGHT; AT THIS LATE HR? WE CLRED THE END OF THE CONCOURSE AND COULD SEE OUR GATE WAS OPEN. WE TAXIED INTO THE GATE; DEPLANED; AND RAN OUR CHKLIST. THE AIRPLANE WAS HANDED OFF TO MAINT AND WE WERE FINALLY DONE. THEN CAME THE MESSAGE TO CALL THE TWR. THE TWR CTLR WAS ALMOST APOLOGETIC WHEN HE ASKED IF I REALIZED THAT WE HAD LANDED ON RWY 13L. I WAS SHOCKED. I SAID; 'NO ARE YOU SURE?' MY FO AND I COULDN'T BELIEVE IT. WE HAD LANDED ON THE WRONG RWY. I SPENT MANY SLEEPLESS HRS REFLECTING ON THE EVENTS LEADING UP TO OUR ARR. HOW COULD WE BOTH HAVE MADE THIS MISTAKE? THE FOLLOWING FACTS BECAME APPARENT. WE WERE A TIRED CREW ON THE LAST LEG HOME AFTER A LONG DAY FILLED WITH LENGTHY DELAYS AND BAD WX. IN THE LAST 20 YRS; I HAD FLOWN INTO MDW A THOUSAND TIMES BEFORE WITHOUT ANY PROBS; BUT I HAD NEVER FLOWN A VISUAL APCH TO RWY 13C AT NIGHT FROM THAT DIRECTION. I ACCEPTED A CLRNC THAT KEPT US HIGH AND TIGHT AND I GOT BUSY TRYING TO CONFIGURE AND DSND WHILE KEEPING THE ACFT CLOSE TO THE ARPT. YES; WE HAD BRIEFED THE ILS BACKUP AND OUR RADIOS WERE SET; BUT I WAS SLOW TO SET MY HSI SWITCH AND MY ATTN GOT DIVERTED OUTSIDE FLYING THE APCH. SUPPLEMENTAL INFO FROM ACN 616444: WE CONFIGURED AND DSNDED MAKING L TFC TO RWY 13C VISUAL. WE BOTH HAD THE ILS RWY 13C DIALED IN. I REMINDED THE CAPT ABOUT THE BEFORE LNDG CHKLIST AND ACCOMPLISHED IT PRIOR TO THE 1000 FT CALL; STICKING TO STABILIZED APCH CRITERIA. MDW TWR CLRED US TO LAND AND MY CAPT FINISHED TURNING FINAL ONTO THE RWY LIGHTS. (AS HE WAS DOING THIS; I NOTICED THE LOC MOVING TOWARDS CTR AND THEN BEGAN TO PAY MORE ATTN TO HIS GS AND DSCNT.) I CALLED HIM 1 DOT HIGH AND THEN HE NOTICED HIS NAV WAS STILL IN LNAV POS. HE CORRECTED THE SWITCH POS AND CORRECTED HIS DSCNT AND WE MADE A NICE LNDG WITH MINIMAL BRAKING WITH A TURN OFF AT THE END. TWR WAS LOOKING FOR US AND WANTED US TO CALL THEM. TWR INFORMED US THAT WE HAD ACTUALLY LANDED ON THE L RWY AND NOT THE CTR. THEY WANTED US TO BE AWARE OF THIS AND BE MORE CAREFUL. THE TWR HAD INFORMED US THERE WAS NO HARM DONE AND IT WOULD BE LIKE THAT PHONE CALL AND INCIDENT NEVER HAPPENED. THE BIGGEST CONTRIBUTING FACTORS TO THIS WOULD HAVE TO BE; IN MY OPINION; FATIGUE; SHOOTING AN APCH NOT USED TOO OFTEN; AND A BIT OF COMPLACENCY.