MD80 CREW AND A DASH 8 HAD AN NMAC ON THE EXPRESSWAY VISUAL RWY 31 APCH TO LGA.

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WHILE FLYING THE EXPRESSWAY VISUAL TO RWY 31 (CLR SKIES; VISIBILITY 10+ MI); WE WERE VECTORED BEHIND A B757; WHO WAS IN TURN VECTORED WIDE BY TWR. WE WERE VECTORED THROUGH THE RWY CTRLINE AND WERE SLIGHTLY R OF CTRLINE ON THE VASI'S DSNDING THROUGH 700 FT WITH CLRNC TO LAND. THE B757 WAS ABOUT TO TOUCH DOWN. DASH 8 WAS CLRED FOR A VISUAL LNDG BEHIND US. FO NOTICED DASH 8; WHO WAS SLIGHTLY BEHIND US ON A L BASE; TURN SHARPLY TOWARD THE RWY. DASH 8 APPARENTLY THOUGHT THE LNDG B757 WAS US AND; WITH HIS R WING UP; DID NOT SEE US ON FINAL. WITH OUR ACFT FULLY CONFIGURED AND BELOW 700 FT; OUR TCASII WAS INHIBITED; BUT DASH 8'S DOT WAS SUPERIMPOSED OVER OUR L WING AND AT OUR ALT ON THE TCASII DISPLAY (WE WERE DISPLAYING 5 MI SCALE). FO POINTED OUT THAT DASH 8 WAS COMING RIGHT AT US. I TOOK A QUICK GLANCE TO MY L AND IMMEDIATELY ORDERED A BREAKOUT TO THE R (N). FO; WHO WAS FLYING; BEGAN A CLBING R TURN; IT SEEMED LIKE 10-15 SECONDS BEFORE I COULD GET THROUGH TWR FREQ CONGESTION TO CALL THE GAR AND DECLARE A NEAR MISS WITH THE TWR. I ESTIMATE THAT WE CAME WITHIN 300-500 FT OF THE DASH 8 ACFT; BUT THIS IS DIFFICULT TO JUDGE AT NIGHT. WE WERE BOTH ON SHORT FINAL; BELOW 700 FT; LNDG ON THE SAME RWY; SIDE-BY-SIDE. TWR APPARENTLY DID NOT OBSERVE THE EVENT; SINCE NO GAR OR BREAKOUT WAS DIRECTED BY THEM. ADDITIONALLY; THEY DID NOT IMMEDIATELY RESPOND TO; OR SEEM AWARE OF OUR GAR; UNTIL I NOTIFIED THEM ON THE RADIO. WE WERE VECTORED FOR ANOTHER APCH AND LNDG WITHOUT INCIDENT. I NOTIFIED THE PAX THAT 'WE WERE VECTORED TOO CLOSE TO ANOTHER ACFT FOR A SAFE LNDG; AND ALTHOUGH WE WERE IN NO DANGER; WE ELECTED TO GO AROUND AND SET UP FOR ANOTHER APCH FOR THEIR SAFETY.' FO SHOULD BE COMMENDED FOR HIS SITUATIONAL AWARENESS AND PROMPTED AND CORRECT ACTIONS TO AVOID WHAT COULD WELL HAVE BEEN A TRAGIC EVENT. HE HAS BEEN WELL TRAINED AND IT SHOWED.