Goals from Lee Haywood, Henry Adams and Alex Graham were enough to secure a deserved 3-1 win for Greg Wood's team, who now face Milton Keynes Lightning in Sunday's play-off final.
The Steeldogs had seen off the Tigers over two legs earlier this season to lift the National Cup and found their latest encounter with Tom Watkins's league champion equally tough.
After a goalless first period, the deadlock was broken by Haywood at 28.58, with Adams doubling the Steeldogs' advantage just under 10 minutes later.
That is how it looked like staying as a disciplined Steeldogs held the Tigers at bay, only for Andy McKinney to ensure some late drama when he halved the deficit with 90 seconds remaining.
But, with goaltender Brad Day pulled in their attempt to force the game into overtime, the Tigers paid the penalty when Alex Graham ensured passage through to Sunday's showdown with an empty-net strike with 17 seconds remaining.
Milton Keynes also had to do it the hard way - as expected - against Peterborough Phantoms - coming from 4-2 behind at the end of 40 minutes to win a thrilling contest 6-5.