Midfielder Ryan Gilligan drove the Cobblers ahead from 20 yards on the stroke of half-time but Elphick struck 12 minutes after the break by heading in an outswinging corner from substitute Seb Carole.
Both sides played the remaining 25 minutes with 10 men after Brighton utility man Adam Virgo and Adebayo Akinfenwa of Northampton were dismissed for violent conduct after tangling on the halfway line.
Substitute Craig Davies headed against the crossbar for Brighton late on and also blazed wastefully wide when clean through in stoppage time.
Northampton top scorer Akinfenwa had an early snap-shot saved low down by Michel Kuipers before Seagulls skipper Nicky Forster's goal-bound header was dealt with by Northampton keeper Ron-Robert Zieler.
The Seagulls had a lucky escape when Gilligan miscued in front of goal after Leon Constantine had combined with Akinfenwa. The draw halts a depressing run of four successive defeats for Town.