Theaker bagged 5-37 as the hosts were dismissed for 127 in 34 overs, Josh Bowes scooping 3-33 and Simon Bowes 2-28.
Corey Towell top-scored with 44 for the home side, Tom Ward adding 23.
Josh Bowes top-scored with 30 to cap a superb day, while lower-order batsmen Gary Sivills (11no), Paul Theaker (12) and Billy Welford (13) helped Staithes edge home.
Mulgrave are only a point behind Staithes after opening batsman Chris Batchelor hammered another century in his team's seven-wicket triumph at Staxton.
The hosts posted 209-9, mainly thanks to impressive knocks from Chris Dove (79) and the in-form David Morris (50), Craig Thompson and Chris Knight snapping up three wickets apiece.
Batchelor led the way with an excellent 130 from 123 deliveries, including 16 fours and three sixes, putting on 137 for the first wicket with Knight (42) and 67 for the second wicket with Liam Cannop (32).as Mulgrave eased to victory with 3.5 overs and seven wickets to spare.
Folkton & Flixton 2nds opened their account for the season with a two-wicket win at home to Ebberston, thanks mainly to a cracking all-round display from Connor Stephenson.
The latter opened the bowling for Flixton and took 4-29 as Ebberston posted 176-7, Peter Kay also taking two wickets.
Ebberston were in deep trouble at 6-3, Eddie Swiers hammering 69 and Adam Machen 43.
Opener Stephenson led the way with 52 in reply, skipper Jack Walmsley hitting 27 and Kay's 39no seeing the hosts across the winning line, despite James Boyes 3-39.
Heslerton skipper Sam Triffitt led by example with a stunning century as his side won by four wickets at Brompton.
Triffitt smashed seven fours and seven sixes in his unbeaten 106 from 98 balls, steering the visitors to victory with 167-4 from 42 overs, Tom Pateman and Arthur Aston taking two wickets apiece.
Adam Spaven earlier secured figures of 4-24 as the hosts made it to 163-9, Joe Barker top-scoring with 42 from 110 balls, Pateman chipping in with 35 and Tom Fletcher-Varey 26.
Seamer stormed to a 120-run success at Bridlington 2nds.
Opener Archie Graham smacked a superb 79, skipper Gregg Chadwick adding 38, Darrol Lewis 28 and Adam Morris 25 as the visitors racked up 214-8, Sam Edmundson, Tom McMeeken and Andy Smith taking two wickets apiece.
Matty Morris then ripped through the Brid batting order with 4-37, with Matty Walters and Adam Morris bagging two wickets apiece as the hosts slipped to 94 all out, Edmundson top-scoring with 39 to complete a great all-round day despite the defeat.
A great all-round team effort steered Scalby to a six-wicket win at home to Filey.
Despite a superb 100 from Tom Fitzgerald, the visitors were dismissed for 174, but considering Filey were 12-5 and 63-7 this was a brilliant effort from Fitzgerald and the lower order batters, number nine bat Kyle Scaife adding 21 and number 10 Stu Neilson 12no.
Paul Hesp recorded stunning figures of 3-7 in 10 overs, with Matty Jones (2-41), Lachlan Scales (2-30) and Liam Cousins (2-42) also chipping in.
Opener Brett Cunningham and Fraser (64no) then laid the foundations for the Scalby win, skipper Chris Malthouse also weighing in with 26 as the hosts eased to victory.
Jordan Allanby and Joe Canning snapped up 4-11 and 4-26 respectively as Great Habton raced to a rapid nine-wicket win at home to Thixendale to bag top spot in Division One.
Tom Pickering (17no) and opener Les Milburn were the only Thixendale batsmen to reach double figures as they were skittled for just 77 in 35 overs.
Thornton Dale remain in the title hunt after their 25-run win at Wykeham.
Opener Lewis White struck 44 and Matthew Knowles 37 as Dale posted 164-8, Tom Owen was the top Wykeham bowler with 3-54, Mike Dugdale and Balraj Balachandran chipping in with two wickets each.
Gareth Hunt and Colin Lockwood then ripped through the home batting order with 4-32 and 4-23 respectively as Wykeham were all out for 139, skipper James Bryant's explosive 53 from 35 balls, including six fours and three sixes, Sam Owen (31) and Dave Pearson (19) adding their support, but it was not enough to halt the visitors charging to victory.
Mike Artley's 70 not out steered Sewerby to a seven-wicket success at Ebberston 2nds.
Openers Dan Artley (32) and Steve Kitching (26) also impressed as Sewerby overhauled the home side's 165-6.
Jacob Warters' 79 had earlier been the top knock for the home side, Jon King (33no) and George Hardie (31) also weighing in while Ash Porter sparkled with 4-25 in 10 overs.
Forge Valley lost by 20 runs at Sherburn, while Cloughton conceded again, this time Fylingdales being the recipients of the 22-point haul.