Seeking a first T20 Blast crown, Yorkshire raced out of the blocks against Nottinghamshire at a sweltering Headingley as Lyth and Will Luxton (38) shared an 89-run opening stand inside the opening eight overs.
Jonny Bairstow (32) and Logan van Beek (28) helped to set the already-qualified visitors a target of 194.
Root’s two wickets, along with Andrew Tye (3-18) and Hassan Ali (2-30) helped reduce Notts to 107-7 but some late hitting from Dillon Pennington (37) threatened to derail the Yorkshire victory charge before he became Tye’s second victim.
At Old Trafford, Lancashire made hard work of overhauling Durham’s 141 all out after they had won the toss and elected to bat.
Only Colin Ackermann (66 not out) was able to get to grips with some tight Lancashire bowling as Shadab Khan and Saqib Mahmood claimed three wickets each.
The home side seemed to be cruising at 117-4 at the start of the 17th over but a three-wicket burst from Ben Raine (4-21) left the nerves jangling among home supporters, but Keaton Jennings (41 not out) steered them over the line with two balls remaining.
Lancashire now need Essex to lose at Surrey in one of Sunday’s late games to reach the quarter-finals.
Derbyshire Falcons avoided the wooden spoon and consigned three-times Blast champions Leicestershire Foxes to bottom spot in the group with a crushing seven-wicket victory.
Falcons captain Aneurin Donald struck a career best 91 as the home side easily overhauled the Foxes 171-8 with Ashton Turner’s 79 the mainstay for the visitors, while Akif Javed returned T20-best figures of 4-23.