The Tigers, who notched their ninth straight win, scored the first 33 points and five goals of the game, but had to hold on desperately to record a 10.8 (68) to 9.11 (65) victory.
The Swans kicked seven goals to two to briefly hit the front in the third quarter, but the Tigers led for all but a few minutes of a compelling and fiercely fought game.
It’s the first time in almost 40 years the Tigers have made the finals in successive seasons.
Sydney had their chances in the final quarter, twice getting within two points in a tension-filled finale.
Jack Riewoldt finished with four goals, three of them in the Tigers’ furious early onslaught.
Brett Deledio kicked three goals and got 27 touches, while Trent Cotchin logged 29 possessions.
Ivan Maric dominated the hitouts, with Sydney replacing debutant ruckman Sam Naismith in the third quarter.
Dan Hannebery secured 33 disposals and Tom Mitchell 30 for Sydney who had just one multiple goalkicker in Sam Reid, who finished with two majors.
The Tigers’ first quarter score was the biggest conceded in an opening term by Sydney all season.
The Swans suffered a blow before the game when star forward and Coleman Medal leader Lance Franklin withdrew with knee soreness.
Despite the loss the Swans’ superior percentage ensures they will finish the regular season first.