The teams were tied at 5-5 after last week’s first leg, but goals by Willie Nicolson (2), Robbie Hill, Conor Duncan and Reece Cochrane sealed a 5-3 win for the Kestrels in the reverse fixture.
Aberdeen Lynx also progressed to the last four, although they were given an almighty scare by Dundee Tigers before securing their spot.
Lynx led 7-3 going into the second leg, but the Tigers fought back on home ice to tie the aggregate scores at 8-8.
Penalty shots were required to separate the teams and it was Lynx who emerged victorious with Iain Malcolm and Christian Johnson sealing a dramatic win.
The play-off semi-finals take place at Fife Ice Arena on Saturday, 8th April, with Kirkcaldy facing Paisley Pirates and Aberdeen meeting Dundee Comets.
The final is scheduled for the following day.
Aberdeen Lynx 7-3 Dundee Tigers
Dundee Tigers 5-1 Aberdeen Lynx (SO) (agg 8-9)
Edinburgh Capitals SNL 3-5 Kirkcaldy Kestrels (agg 8-10)
(Image permission: Ian Coyle)