The SunRisers Leeds star took 2-26 before leading a dogged run chase with an unbeaten 59 as her side pushed Rockets all the way before falling short by five runs.
Rockets' own Aussie ace, captain Ashleigh Gardner, played a key role towards the end, conceding just five runs off as many balls to help ensure her side stayed just beyond reach.
Rockets had earlier reached 7-139, led by England batter Sophia Dunkley with a half-century at Nottingham.
Dunkley produced nine fours during a 33-ball innings of 56 and put on 76 for the second wicket with fit-again England captain Nat Sciver-Brunt, who made 33.
A strong fight back by SunRisers restricted Rockets after they were 1-84, with Sutherland claiming two crucial wickets, including Dunkley, to slow the home side's progress. Another Aussie, Jess Jonasson, took Sciver-Brunt in her pair of wickets.
When SunRisers batted, Aussie Phoebe Litchfield and Dani Gibson were out in quick succession leaving the onus on Sutherland. Two sixes helped take 23 runs off a five-ball spell from Georgia Elwiss.
However, Gardner only conceded five during the penultimate five deliveries of the match to leave 17 required off five balls. It proved a step too far for Sutherland and Sunrisers, who were restricted to 5-134.
In the day's other match, Meg Lanning made 43 from 31 balls and took three catches as her Manchester Super Giants side piled on the pain for MI London at the Oval.
Super Giants won with 28 balls to spare leaving MI London still winless.
England spinner Sophie Ecclestone dismissed MI London openers Alice Davidson-Richards and Hayley Matthews for ducks inside the opening eight deliveries as the Londoners were bowled out for 92.
Ecclestone also impressed in the field, catching MI London's top scorers Kira Chathli (18) and Aussie Nicola Carey (17) off Kathryn Bryce and Ryana MacDonald-Gay respectively, before producing a direct hit to run out Tara Norris.
MacDonald-Gay claimed the final wicket, bowling Kirstie Gordon, to finish with figures of 3-19. Ecclestone returned 2-7, while another Aussie, Maitlan Brown, took 2-18.
Lanning featured in an opening stand of 71 with Smriti Mandhana (34), putting the visitors firmly in control before Mady Villiers sealed their third win of the campaign with a four.
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