B737 CAPT REPORTS INADVERTENTLY USING LNAV TO FLY LOC RWY 27 AT SAN.

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I WAS THE PF AND WE WERE DSNDING ON A VECTOR TO JOIN THE LOC 27 APCH AT SAN. CEILINGS WERE NEAR MINIMUMS FOR THE LOC APCH AND WE HAD BRIEFED A COMPANY PROCS APCH -- FO FLYING AND CAPT LNDG. MY LAST ACT AS PF WAS TO SET THE ACFT UP FOR AN LNAV INTERCEPT TO THE 27 LOC OUTSIDE OF SWATT. I GAVE THE ACFT TO THE FO AND HE WAS AWARE OF THE FLT MODE SELECTIONS. WHILE NOT SPECIFICALLY BRIEFED; I BELIEVED HE WAS AWARE OF THE INITIAL PLAN TO FLY THE LOC COURSE IN LNAV MODE (DUE TO THE NOTORIOUSLY WANDERING LOC FOR THIS RWY) WITH THE IDEA OF SWITCHING TO LOC MODE ON THE MCP PRIOR TO THE FAF. I SHOULD HAVE MADE THIS CLEARER IN MY BRIEFING; BECAUSE NEITHER OF US CAUGHT THAT LNAV WAS STILL SELECTED AS WE BEGAN OUR DSCNT INSIDE REEBO. JUST AS WE WERE APCHING THE MDA AND BREAKING OUT OF THE OVCST; THE TWR CTLR RPTED A LOW ALT ALERT ON US. AT THAT SAME TIME I ACQUIRED THE RWY; BUT WAS SURPRISED TO SEE IT OVER AT ABOUT THE 1:30 O'CLOCK POS. A QUICK GLANCE AT THE HSI NEEDLE (STILL SHOWING RAW LOC DATA SINCE WE WERE FLYING A -700) INDEED SHOWED US A LITTLE MORE THAN 1 DOT L OF COURSE. I TOOK OVER FLYING AND THE FO ACKNOWLEDGED THE TWR'S ADVISORY. I DISCONNECTED THE AUTOPLT AND MADE A CORRECTION BACK TO THE RWY CTRLINE. THE REST OF THE APCH AND LNDG WERE STABILIZED AND UNEVENTFUL. NO EGPWS WARNINGS/CAUTIONS WERE OBSERVED THROUGHOUT THE APCH. I NEED TO FOLLOW THE COMPANY PROCS FOR LNAV TRANSITIONS TO INST APCHS; EVEN IF IT MEANS SOME HUNTING OF THE ACFT WHEN TRACKING LOCS LIKE RWY 27 AT SAN.