The pair clearly relished batting on home soil as Lightning racked up a total of 320 - the highest in the competition history.
Anderson struck 12 boundaries in a top score of 76, sharing in a second wicket stand of 73 with skipper John Mooney (30) after Kevin O'Brien had been dismissed by Mark Adair (2-44).
Kane, the newest Irish international, gave the innings real impetus at the end, as he smashed 57 from just 33 balls, clearing the ropes four times.
Dom Joyce - the third Merrion player in the Lightning line-up - batted with great fluency making a breezy 36 from 35 balls (5 fours, 1 six).
The Knights cause wan't helped by the concession of an incredible 62 extras - 39 of which were wides in a bowling display to forget.
Shane Getkate (4-48) was the most succesful of the attack, while there were two wickets apiece for Mark Adair (2-44) and Peter Eakin (2-64).
The Knights reply started in disastrous fashion as Chris Dougherty (8), James Shannon (1) and Lee Nelson (0) all departed in quick succession to leave them reeling on 19 for 3.
The Knights' hopes of getting anywhere near the imposing total lay with CIYMS professional Rassie van der Dussen - the South African coming off the back of successive centuries in 48 hours in the NCU cup final.
However, he made just 21 before being trapped lbw by John Mooney (2-13), and from then it was really a matter of damage limitation for the Knights.
Skipper Andy White top scored with 57 from 84 balls (7 fours), while Mark Adair hit the only six of the innings in an entertaining 22, but it was very much a case of too little, too late.
The Knights were dismissed for 162, with Eddie Richardson taking 3 for 26, while John Anderson completed a fine all-round display to finish with 2 for 17.
Lightning will clinch the title if they beat the Knights next Sunday at Waringstown in the return fixture.
HANLEY ENERGY IP50 CUP
At Angelsea Road,
LEINSTER LIGHTNING 320 all out (49.5 overs, J Anderson 76, T Kane 57, D Joyce 36, J Mooney 30, S Getkate 4-48, M Adair 2-44, P Eakin 2-64)
NORTHERN KNIGHTS 162 all out (33.5 overs, A White 57, M Adair 22, R van der Dussen 21, E Richardson 3-26, J Mooney 2-13, J Anderson 2-17)
Leinster Lightning beat Northern Knights by 158 runs
