The Strikers did a tremendous job with the ball restricting the Scorchers to just 9-159 despite some impressive late hitting from Coulter-Nile who scored 42 from just 25 balls.
Coulter-Nile then also bowled well taking 2-28 from his four overs for the Scorchers, but the total was never likely to be enough and with Klinger remaining 86 not out and after 31 from Alex Hales got things started well, the Strikers cruised to victory scoring 4-164 after 19 overs.
The result means that the Strikers remain unbeaten after two matches to move to the top of BBL 03 table while the Scorchers have just the one victory from three games after having played in the last two finals of the competition.
Scorchers captain Simon Katich won the toss and decided to bat first at the Adelaide Oval but the visitors suffered an early blow with Shaun Marsh out for two when run out by Johan Botha on the same day he was named in Australia's one-day squad.
Katich and Sam Whiteman got things rolling for Perth, though, and combined for a 57-run second wicket partnership from just 38 balls before Whiteman was out for 19 from 15 balls to the bowling of young leg-spinner Adam Zampa.
Katich then fell just five balls later to the bowling of Michael Neser with the veteran out for a solid 36 from 30 deliveries with four boundaries and a six.
The Scorchers at that stage were 3-63 in the ninth over but things began to unravel soon after with Mitch Marsh out for 13 (11 balls), Ashton Turner for 25 (16) and Yasir Arafat for a duck.
Perth had gone from 3-87 to losing four runs for just 25 runs in a four-over period that put them right on the back foot.
Tail-enders Alfonso Thomas (2 from 7), Brad Hogg (0 from 1) and Michael Beer (1 from 3) all couldn’t do anything to help the Scorchers' cause, but Coulter-Nile could as he teed off with three massive sixes and three boundaries in his 42 from 25 balls as the Scorchers ended up with a below-par 9-159.
Neser finished with 3-27 from four overs for Adelaide with Shaun Tait taking 2-27 from four, Zampa 2-28 from four, Ben Oakley 0-50 from four and Botha 0-22 from four.
The Strikers' chase got off to the perfect start when Klinger hit left-arm spinner Beer for four from the first ball past mid-off and then Hales also got off the mark with a boundary off Beer as the home side scored 10 from the first six balls.
Englishman Hales then continued on hitting five boundaries and a six as he took apart Pakistani quick Arafat before also falling to the same bowler for 31 from 20 deliveries.
The Strikers were 1-44 after four overs when the wicket fell and Phil Hughes was soon back in the pavilion also for eight off seven balls when he fell to the bowling of Coulter-Nile and to a brilliant one-handed diving catch in the deep from Tim Armstrong.
Captain Botha then struggled as well making just six before being bowled by Beer and Callum Ferguson never got going falling for 10 before Nathan Reardon joined Klinger at the wicket.
It was never the smoothest run chase from the Strikers, but the small nature of the total meant there was never any danger of them coming up short.
The longer Klinger was at the creaser the easier he made it look as well as the veteran right-hander finished up with a superb 86 not out from just 55 deliveries with five fours and four sixes.
Reardon also stayed with him until the finish on 16 from 11 balls with a six.
Coulter-Nile finished up with 2-28 for the Scorchers while Beer had 1-31 from four overs, Arafat 1-42 from four, Hogg 0-26 from four and Thomas 0-30 from three.