After winning the toss, Finley elected to bat and were met by a disciplined Rhinos bowling and fielding performance that restricted the visitors' scoring opportunities throughout their 40 overs.
Finley's opening batter Jonty King was removed early without scoring when a catch was held in the field.
The Cats then steadied through a solid second-wicket partnership between other opening batter Marcus Anderson and Jono Cattell.
Marcus Anderson was dismissed for 45, while Jono Cattell followed for 32 both out caught.
Captain Harrison King, Ryan Bauer and Jed Flanagan were all out for single digits for Finley.
However Ben Nisbet anchored the Finley total with an unbeaten 40 as the visitors finished on 7-150 from their 40 overs.
Defending 151 for victory, the Cats had the early breakthroughs .
Shibin Benny had the first Rhinos opener out caught for three by Marcus Anderson.
Bailey Coombs then struck removing the opener, first drop for ducks and fifth in the batting order for one all out bowled.
The Deni Rhinos responded with a big fifth wicket partnership to steady their innings.
Jonty Tubb played an important hand of 32 for the Rhinos before being caught off the bowling of Justin Crowley, while Lachlan Marshall was bowled without scoring shortly afterwards bowled by Crowley.
At 6-111 after 28 overs, the Rhinos still required 40 runs from the remaining 12 overs with four wickets in hand.
The match swung back in favour of the home side through a pair of productive overs that lifted the score to 6-129 after 30 overs.
The Rhinos continued to edge closer to the target and were 6-140 after 33 overs when Marshall's innings came to an end for 72.
He was caught and bowled by Coombs who provided the breakthrough.
With the result still not secured, the Rhinos held their nerve, reaching 7-151 in the 34th over to hand the Cats a close fought season opening three-wicket loss.
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