Yorkshire survived a scare after Unicorns had threatened to pull off a shock victory in their CB40 League Group C encounter.
Chasing a modest revised target of 162 in 37 overs at Headingley, the hosts lost four wickets for seven runs in the space of 22 deliveries to sit well behind the required rate at 78 for five in 18.4 overs when rain caused a brief interruption.
But Gary Ballance and Azeem Rafiq spared Yorkshire's blushes, the pair putting on an unbroken 91 for the sixth wicket to haul Yorkshire back into the match.
Ballance kept his nerve with a fine unbeaten 69 and he was well supported by Rafiq, who made 34, as the hosts went on to win by five wickets with three overs remaining.
Earlier, Unicorns, put into bat, were never able to break free from the stranglehold imposed on them by Ryan Sidebottom and Adil Rashid.
They would not have reached 150 for six off their 37 overs but for an unbroken seventh wicket stand of 56 between skipper, Keith Parsons, and Bob Woolley.
At 94 for six in 27 overs, a complete slump was prevented by Parsons and Woolley, but a sudden break for rain at 141 for six in 36.1 overs brought about a reduction in the overs.
With only five balls remaining on the resumption, Parsons immediately belted Sidebottom for six over mid-wicket. His unbeaten 48 came off 60 deliveries with two fours and a six while Woolley made 28 not out with three fours.
Rashid's final figures of 3-24 followed hot on the heels of his career-best 4-38 against Northamptonshire in the previous match.