Ill-discipline hurt the hosts with Hickey nailing two early penalties before former Auckland pivot Moeke got the Stags on the board to make it 6-3 heading into the second quarter.
Southland continued to pay the price for offside play, with Hickey extending Auckland's lead before a big run down the left touchline from No6 Joe Edwards created the chance for Ben Lam to run in the opening try.
The Stags received a boost when a wayward pass from Auckland's Gorge Moala gave centre Keiran Moffat a timely intercept try, with Moeke converting to help narrow the margin to 16-10 at halftime.
A second Moeke penalty gave Southland the ideal start to the second-half, before Elliott Dixon crossed out wide for their second converted five-pointer, after Auckland's Bryce Heem spilled an attacking high-ball.
Momentum continued the Stags' way with Auckland turning it over to come under more pressure before a third Moeke penalty made it 23-16 with less than 30 remaining.
Some expansive play from Auckland looked to have earned reward but Southland replacement James Schrader snatched the ball from Lolagi Visinia's grasp as he attempted to ground the ball ingoal.
The visitors persisted with good scrum pressure and forward drives attracting defenders before Moala crashed over for their second, with Hickey again converting to level the scores with 13 remaining.
Moeke had the chance to push his side into the lead when Southland were awarded a ruck penalty inside the final 10 minutes but Moeke's attempt at goal bounced away off the upright.
Auckland halfback Mitch Hunt was entrusted with a last-minute penalty goal but he skewed the 40 metre shot wide, much to the relief of the home crowd.
Southland 23 (Keiran Moffat, Elliot Dixon tries, Moeke 2 cons, 3 pens)
Auckland 23 (Ben Lam, George Moala tries, Jono Hickey 2 cons, 3 pens)
