ABRUPT EVASIVE ACTION REQUIRED BY ACR MLG FLT CREW TO AVOID COLLISION WITH LIGHT TWIN; OPPOSITE DIRECTION.

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WE HAD BEEN CLRED TO DSND TO 5000' MSL BY BAY APCH (135.4) ON A 240 DEG HDG TO INTERCEPT THE LOC TO OAK RWY 29. APCH CTL ASKED OUR ALT AS WE APCHED 8000' MSL; AND I ANSWERED; 'PASSING 8000'.' APCH CTL SAID; 'TFC AT 1 O'CLOCK; 4 MI; 7200'.' I SAID TO THE F/O; 'LET'S LEVEL OFF;' AND HE LEVELED OFF AFTER DISCONNECTING THE AUTOPLT. AS WE LEVELED OFF AT ABOUT 7600'; THE F/O SAID; 'THERE HE IS!'; AND WE BOTH APPLIED AILERON CONTROL FOR AN ABRUPT RIGHT BANK TO MISS THE ACFT. HE WAS AT OUR 12:30 POS; SAME ALT; AND HDG APPROX 120 DEGS. THE ACFT WAS A WHITE LIGHT TWIN WITH BLUE STRIPE(S); LOW WING WITH WINGLETS; THAT PASSED ABOUT 200' OFF OUR NOSE WITH NO EVASIVE ACTION OF HIS OWN. I FEEL CONFIDENT WE WOULD HAVE COLLIDED W/O EVASIVE ACTION. DURING CONVERSATION (AFTER LNDG AT OAK) WITH TRACON SUPVR; HE WAS DISSATISFIED THAT THE CTLR HAD NOT HANDLED THE CONFLICT DIFFERENTLY BECAUSE THEY HAD BEEN TALKING TO THE OTHER ACFT. MY OPINION WAS THAT THE TFC SHOULD HAVE BEEN CALLED TO US FIRST AND/OR AN INSTRUCTION TO LEVEL OFF; RATHER THAN FIRST REQUESTING OUR ALT. APPARENTLY; INTERMITTENT DATA BLOCKS ON THE CTLR'S SCREEN MADE IT UNCLEAR AS TO THE CONFLICT. MORE AGGRESSIVE CTLR ACTION COULD HAVE NEGATED THE NEED FOR ABRUPT EVASIVE ACTION; WHICH WAS THE ONLY FACTOR IN AVOIDING A CATASTROPHE.