WRONG RWY APCH LNDG. UNAUTH LNDG IN A NIGHT OP.

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WE HAD FLOWN FROM ENW TO MSN AND HAD BEEN HANDED OFF FROM MSN APCH TO MSN TWR. PRIOR TO ENTERING THE L DOWNWIND FOR RWY 13 AS INSTRUCTED; I ASKED THE TWR TO TURN UP THE LIGHTS FOR RWY 13 SINCE MY STUDENT WAS UNCERTAIN OF THE RWY'S LOCATION. THE TWR COMPLIED AND TURNED UP BOTH RWY 13 AND RWY 18 LIGHTS. THE WIND WAS RPTED TO BE FROM THE E AND AS WE ENTERED DOWNWIND; I MADE MENTION OF THIS FACT TO THE STUDENT AND SUGGESTED WIDENING OUT OUR PATTERN. THE STUDENT WAS PREOCCUPIED WITH THE BEFORE LNDG CHKLIST AND DID NOT RESPOND WITH ANY MAJOR CORRECTIVE ACTION. AS WE PASSED THE END OF THE RWY; THE PWR WAS REDUCED AND FLAPS SET AS NORMAL. WE BEGAN A STANDARD L BASE (ALREADY CLRED TO LAND RWY 13) AND I WAS ALREADY ANTICIPATING THE POSSIBILITY OF OVERSHOOTING THE RWY ON BASE DUE TO OUR POS AND WIND CONDITIONS. AS WE STARTED TO ROLL OUT ON BASE I SAW A LIT UP RWY OFF TO OUR L SIDE. I IMMEDIATELY PERCEIVED THIS TO BE RWY 13 AND THAT WE HAD IN FACT OVERSHOT THE RWY ON BASE. I TOOK OVER CTL OF THE ACFT AT THIS POINT AND MADE MENTION OF OUR POOR POSITIONING TO THE STUDENT AND THAT I WAS GOING TO RE-CTR US FOR A CONTINUED APCH TO RWY 13. AT APPROX 1/4 - 1/8 MI OUT ON FINAL APCH; I INSTRUCTED THE STUDENT TO TAKE CTL AGAIN; YET I STAYED ON THE CTLS (STAYED WITH THE CTLS -- SHADOWED THE STUDENT'S CTLS) IN CASE HE NEEDED HELP WITH THE XWIND LNDG. THE LNDG WAS COMPLETED SUCCESSFULLY AND AS WE ROLLED ON THE RWY; I INSTRUCTED THE TWR WE WERE GOING TO FBO. THE TWR REPLIED THAT WE HAD LANDED ON THE WRONG RWY; WE WERE CLRED FOR RWY 13 BUT HAD LANDED ON RWY 18. THE TWR SAID SOMETHING TO THE EFFECT THAT 'BUT THAT IS OK; JUST TAXI OFF ON C AND CONTACT GND ON POINT 9.' WE DID AS INSTRUCTED. IN THE SHORT TIME PERIOD IN WHICH ALL OF THIS HAD OCCURRED I LET MY PRECONCEIVED NOTION OF OVERSHOOTING THE RWY INTERFERE WITH MY OWN ORIENTATION AND VISUAL POSITIONING ON BASE AND FINAL FOR RWY 13. HAVING BOTH RWYS LIT UP I UNINTENTIONALLY WENT FOR THE FIRST ONE I SAW; RWY 18.