The former Manchester Utd and Derby defender struck in the 37th minute to cancel out Danny Shittu's 32nd-minute opener and make it a point apiece for both sides.
Southampton came into the match looking to extend their unbeaten run of five league and cup matches and Jamaican striker Ricardo Fuller could have got them off to a perfect start by opening the scoring in only the 5th minute.
The former Portsmouth star would of netted for the second successive match had it not been for the efforts of Rangers keeper Simon Royce who saved with the leg to deny Fuller when clear on goal.
And Fuller was made to pay for that miss later in the half when Shittu opened the scoreing with a bullet header. Shittu was picked out by a pin-point Lee Cook corner and the big centre half headed in the left-hand corner of the goal.
Left back Higginbotham drew Saints level just five minutes later though after catching the Rangers defence napping with a quick free-kick.
Kenwyne Jones was bundeled over on the edge of the penelty area and Higginbothom shocked everybody by driving the ball into Royce's bottom left-hand corner.
Royce prevented Djamel Belmadi putting Southampton into the lead in the 40th minute when Jones squared the ball on the edge of the area but Belmadi's shot from 12 yards was palmed away.
Jones had Saints' best chance of a drab second half with his close-range header that was stopped at the near post and with both sides struggling to create any chances of note, a draw was a fair result on the balance of play.