A B737-300 EXPERIENCES A MAP SHIFT ON ARR TO PIT; AND THE CREW IS MOMENTARILY DISORIENTED.

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I'M A B737-300 CAPT WITH CLOSE TO 11000 HRS IN THE -300 ALONE. MY RESULTANT OVERCONFIDENCE IN MY ABILITY COUPLED WITH MY OVER RELIANCE ON THE DEMONSTRATED NEAR PINPOINT ACCURACY OF THE RNAV SYS; ALMOST GOT ME INTO TROUBLE. DSNDING INTO PIT; ON A DARK BUT CLR VFR NIGHT; ON THE CUTTA 2 ARR; WE WERE SET UP; AS PER THE ATIS; FOR A SUBSEQUENT ROUTINE ILS RWY 28R APCH. BUT FAR AFTER THE APCH BRIEFING AND NEARING 10000 FT; THE CTLR OFFERED RWY 28L. WHICH AS YOU KNOW GETS US TO THE GATE MUCH QUICKER. WELL; IN THE PROCESS OF RECONFIGURING OUR NAV RADIOS TO ILS RWY 28L THE CTLR THEN OFFERED AN EVEN BETTER RWY -- RWY 10L VISUAL. 'WE TOOK THE BAIT.' WE GOT THE RIGHT RWY IN THE FMC BUT IN THE PROCESS OF ME FOCUSING ON BRIEFING THE FO (PF) OF THE NECESSITY TO BE AT 210 KTS AND 10000 FT AT CUTTA; OR ELSE WE WOULD BE TOO HIGH AND FAST TO MAKE RWY 10L; WE DIDN'T NOTICE THAT BOTH OUR NAV RADIOS WERE STILL MANUALLY TUNED FOR ILS RWY 28L. HENCE; NO RADIO UPDATING FOR THE RNAV. YOU GUESS IT -- WE GOT A 'HUGE MAP SHIFT.' THE LIKES OF WHICH I HAVE NEVER SEEN IN ALL MY NEAR 11000 HRS IN THE B737. WE INITIALLY SAW THE ARPT (OR SO IT SEEMED); RPTED IT; AND RECEIVED CLRNC FOR THE VISUAL APCH. SOMEHOW WE MUST HAVE LOST OR GOT CONFUSED AS TO THE WHEREABOUTS OF THE ARPT BECAUSE THE RNAV MAP DIDN'T JIVE WITH WHAT WE WERE LOOKING AT. THE FO SAID HE SAW A MAP SHIFT; I ORDERED HIM TO JUST FOLLOW THE RNAV MAP. HE DID; WE LOOKED UP; 'AND NO ARPT NOR RWY.' I ASKED THE CTLR TO TURN UP THE LIGHTS; SHE SAID SHE DID; 'THEN IT HIT ME.' IT WAS THEN THAT I KNEW THAT MY FO WAS TELLING ME THE TRUTH. I THEN ASKED FOR RADAR VECTORS; AND THE CTLR OFFERED AN MVA OF 2500 FT. WE PICKED UP THE NOW GLARING RWY LIGHTS; HOPPED ON THE PAPI; AND MADE AN UNEVENTFUL LNDG ON RWY 10L.