Their fast progressing seamer Ben Coad finished with six wickets in the second innings and 10 in the match as Notts forlornly pursued a target of 403.
The 24-year-old’s figures, six for 81 in the innings and 10 for 130 in the match.
Notts started the chase at tea on day three and lost eight wickets before the close, including one in the extra half hour.
Tom Moores and Jake Ball, however, forced a final day before playing nicely during the opening hour of the day to post a ninth-wicket stand of 66 inside 16 overs.
They both played some eye-catching strokes, particularly down the ground, before Coad switched ends to the Kirkstall Lane End and immediately uprooted Ball’s off-stump for 30 and had Harry Gurney caught at slip.
Moores finished with 40 not out in 238 all out.
This was Yorkshire’s second match of the season, yet their first action after last weekend’s opening round clash with Essex here at Headingley was abandoned without a ball bowled due a wet outfield.
They were under the cosh at 93 for five during the first morning before recovering to 256 and driving the contest from then onwards, claiming 21 points to three.
Yorkshire coach Andrew Gale was delighted with his side’s ruthless streak. He said: “We’ve spoken a lot about when the game’s in the balance, someone’s got to put their hand up (with the bat), and that’s what we have done in this game. I thought we were ruthless at times.
“There were certain partnerships, Ballance and Leaning in the second innings and ones at the back end of the first innings and second, that took the game away from Notts.
“At some periods, I didn’t think we were at our best. But to win games of cricket, you need to be ruthless when it’s in the balance. That’s exactly what happened in this game. We can take a lot from that.”
On Coad’s 10-wicket haul, Gale added: “Ben’s confident at the minute. He picked up from where he left off (last season). He hasn’t the most fluid pre-season given he was injured (hip flexor) out in South Africa. He’s had little game time. He just goes about his business, he’s very level-headed and works hard. He’s very particular in preparation.”
For Notts, it has been a mixed start to life back in Division One after their bowlers dismantled Lancashire at Emirates Old Trafford last weekend.
They will be looking to bounce back against Worcestershire at New Road, starting on Friday, when England Test bowler Stuart Broad will be available for the first of three matches prior to the early summer series against Pakistan next month.
Yorkshire’s third fixture of the campaign is at Taunton against Somerset on Friday, who started their summer with a home win over Worcester this weekend.
Last season, the White Rose beat the West Country outfit by three runs in a thrilling contest there, and it proved to be crucial as they ended up avoiding relegation to Division Two by just two points.