Barker's side pulled away in the second half having gone in at the break level at 3-3.
Rovers player-boss Barker handed his side the lead, only for Kristian Wilkinson to head Sherburn level.
Dan Simpson tapped Sherburn ahead shortly afterwards, only for Barker to score his second and make it 2-2.
It was soon 3-2 to Rovers, Neil Forsyth firing in, but Sherburn went in level at the break after defender Wilkinson again found the net from another corner.
Rovers pulled away after the break, Barker wrapping up his hat-trick before goals from Myers and Chris Cass made it 6-3 to the away side.
Simpson grabbed his second to give Sherburn hope at 6-4, but Myers hammered in two more goals to wrap up his hat-trick and seal an 8-4 win.
Cass was Rovers' star man while Chris Watson was Sherburn's man of the match.
Scalby kept up the pressure on the leaders with a hard-fought 2-0 win at Falsgrave.
Rob Speight swept home from the penalty spot to hand the Otters the lead 10 minutes into the contest.
That lead was doubled after 30 minutes, player-boss Sam Medd glancing in a header from Grant Elwell's corner to register a rare goal and put his side 2-0 up.
The only action of the second half saw Chris Hannam's scorching effort from long-range cannon back off the bar.
Young keeper Max Tadman was Scalby's man of the match.
Snainton stayed in second spot after they hammered Old Victoria 9-1.
Andy Holt's side cruised to victory as Shane McAuley, Ryan Collins and Sam Turner all scored two apiece and Connor Bell, Jack Heelas and George Hirst also got on the scoresheet.
Central midfielder Regan Hewitt was Snainton's man of the match.
Cayton sealed maximum points with a 5-1 win at home to Fishburn Park Reserves.
Jake Sands scored the only goal of the first half for the hosts, before Jake McAleese doubled Cayton's advantage after the break with a free-kick.
Finlay Morris hit one back for Fishburn, but any hopes of a comeback were quickly dashed by Jake Sands' second and goals from Ryan Jones and man of the match Luke Foster.
Commercial moved further clear from the wrong end of the table with a 7-4 win against FC Rosette.
Macauley Youngson saw his pen saved by Rosette's Jonny Frame early on and it looked like it was going to be the away side's day when Dane Robinson put them ahead minutes later.
Three first-half goals handed Commercial the initiative, Lee Plant getting their first before Luke Priestley hit a brace to make it 3-1.
Al Wray smashed in a penalty to make the score 3-2 at the break.
Commercial fired in three goals after the break to take control of the contest, Michael Hernandez hitting a brace and Priestley wrapping up his treble to make it 6-2.
Another strike from Robinson made it 6-3 and JP Watson fired in to give Rosette hope at 6-4, but Priestley hit his fourth and Commercial's seventh to seal a thrilling win.
Four-goal hero Priestley was star man for the victors, while keeper Frame shone for Rosette.
Ayton and Goldsborough United shared the spoils after a 2-2 draw.
Sean Pinder's side led through Joe Bradshaw's towering header, but Goldsborough were soon level as skipper Ben Watson found the back of the net.
Ian Laing fired Ayton ahead again just before half-time to give his side the lead at the break, but visitors United weren't to be denied a point and they claimed a share of the spoils via Lee Brannan's strike after a defensive error from Tom Clarke.
Tom Varey and Tyler Beck were Ayton's star men.
West Pier Reserves claimed the spoils from an 11-goal thriller against Newlands Reserves in the Reserve League.
Rich Tolliday led the charge for Johnny McGough's Pier side, firing in four, while their other goals came from Jack Brown and a late winner from player-boss McGough, who showed his predatory qualities to fire in from close range after a scramble in the box.
A much-improved Newlands side looked like they were going to get a share of the spoils after bouncing back from 4-2 down to lead 5-4, but they couldn't hang on at the death,
Man of the match Aiden McCallion smashed in a hat-trick, Finlay McGregor scored and Steve Anderson also found the back of the net for Park.
Edgehill 3rds beat league leaders and club rivals Edgehill Reserves 4-2 in a feisty clash played at the Flamingo Land Stadium on Friday night.
Ben David smashed in a hat-trick for the victors, with Kyle O'Toole also registering.
Ryan Link and Robbie Scarborough scored for the Reserves side, but it wasn't enough for them to get the win.
David and player-boss Martin Cappleman were the star man for the Thirds, while Carl Hepples and Josh Wallace impressed for the Reserves.
Filey Town Reserves battled for a 3-2 win at Scalby Reserves.
Max Gage, Joe Gage and Alex Lytollis fired in for the victors, while Matty Turner and Brandon Catherall scored for the Otters.
Joe Gage and Harry Keary shone for Town, while goalscorer Catherall was Scalby's man of the match.
Seamer Reserves hammered Ayton Reserves 8-2.
Chris Stubbings and Byron Hartley handed Seamer a 2-0 lead, but Chris Milburn and Nicko Dunn dragged Ayton back level.
Skipper Dan Jewitt scored to hand Seamer a 3-2 half-time lead and then Sam Walker hit two in the second-half along with goals from Dan Kelly, Ben Mason and Gary Walters that wrapped up a comfortable win for the hosts.
Dan Kelly was man of the match, while Jewitt and Craig Love also impressed.
Ayton's star men were Will Jones and Chris Reddish.