Geale, who also hit the canvas in the second round, began confidently at Madison Square Garden and was not afraid to stand in front of the big-hitting Kazakh.
But his game plan backfired when Golovkin landed a ferocious straight-right hand late in round three.
The Tasmanian bounced up but shook his head when asked by referee Mike Ortega if he was able to continue, with the fight officially stopped at the two minutes and 43 seconds in the third round.
Golovkin's crunching blow was made all the more impressive by the fact it landed a split second after Geale landed a strong right hand of his own.
But the undefeated champion from Kazakhstan somehow kept his balance to land the blow that ended the fight and extended his record to a perfect 30-0.
Geale has now lost two of his last three fights for a career record of 32-3 but there is now uncertainty over the former world champion's future inside the ring.
The Australian survived a bizarre opening round that saw him trip on a camera strap and was allowed to continue for four minutes after the time keeper forgot to ring the bell.
Geale went down early in the second round but replays showed the 33-year-old lost his balance rather than was hit by Golovkin, but there was no disputing the final decision as the reigning champion showed his power in the next round.