Facing the Adelaide Strikers in a straight shootout for a spot in the finals, Perry looked to have all but wrapped up the Sixers' play-off berth when her side batted first at North Sydney Oval on Sunday and finished 4-173.
Opener Perry crunched 111 off 71 balls which included three sixes and 16 fours.
But a late surge from the Strikers led by Bridget Patterson meant the game went down to the wire with the Adelaide side requiring three runs for a win off the final ball.
Sophie Ecclestone was run out as she chased a second run that would have sent the match to a super over, handing the Sixers victory.
The Strikers' season is over with defeat as the Sixers finished the regular season in second spot to stand one win away from a WBBL final against the Hobart Hurricanes at Bellerive Oval on Saturday.
The Sixers will host the winner of the Knockout final between third-placed Perth Scorchers and fourth-placed Melbourne Stars on Thursday.
Named player of the match, Perry had to survive a couple of scares en route to her third WBBL ton.
Perry was caught on 65 only for replays to show Strikers bowler Tahlia McGrath had overstepped the mark.
And more luck shone on the Australian international when, on 91, she glanced a Amanda-Jade Wellington delivery onto her stumps only for the bails to remain intact.
Perry eventually fell in the final over of the Sixers' innings when she ballooned a Eleanor Larosa delivery to Tabatha Saville at deep cover.
Larosa had earlier claimed the wicket of Sophia Dunkley for 54 after the English import had put on a 141-run opening partnership with Perry.
After claiming the scalp of Perry in the final over, Larosa dismissed Alyssa Healy and Ashleigh Gardner as the Sixers set Strikers their target of 174.
The Strikers started slowly and were just 2-60 at the 10-over mark but Patterson had other ideas.
She bludgeoned her way to a 30-ball 50 to leave the Strikers needing 18 off the final over to win.
Patterson whacked Gardner for two fours and a six off the first three balls of the last over before running a single that put Wellington on strike.
Gardner bowled Wellington through the gate to leave Ecclestone needing to hit three to win the match off her first and final delivery.
The English international was run out by Healy as she went in search of the second run that would have extended the match.
The Sixers will learn their finals opponent on Tuesday when the Scorchers host the Stars.
