Two early goals saw the away side take a firm grip of the game.
Youngster Ted Edwards marked his first start for the visitors with a headed goal from a corner after only three minutes, and two minutes later Ryan Link doubled Edgehill's lead.
The lead was extended on the half-hour when Sean Exley cut in from the left and let off a thunderous strike into the far top corner, but joy turned to pain instantly for Exley as he pulled his quad and came off injured at the same time.
The hosts started strongly after the interval and pulled a goal back on the hour mark through Luke Jones.
New Edgehill keeper Kyle Scaife was sent off 10 minutes later for a clash on the edge of the box, then the home keeper Tom Leeson was forced off through injury.
The man advantage only lasted 10 minutes for Jordan Lee's Rovers as a strong challenge from Sam Whitehead led to him being shown the red card.
Eight minutes from time the win was sealed with a great strike from the edge of the box by Joel Ramm which nestled in the bottom corner of the net.
Man of the match for Edgehill was Ryan Link, with Charlie Birley the star man for Rovers.
Filey Town debutant Tyler Beck was the star man in his side's 6-1 home win against Scalby.
A double from Liam Sugden, plus goals from man of the match Beck, Joe Gage, Luke Priestley and Max Gage secured the win for the Clarence Drive club, Josh Beach netting a late consolation for the villagers.
Ben Luntley hit a hat-trick as Newlands earned a 6-2 win at a West Pier side who played 70 minutes with 10 men after the early dismissal of Jordan Gillen.
Pier made a bright start, taking a 10th-minute lead thanks to John Grayston's strike from the edge of the box, but 10 minutes later Gillen was dismissed for a late challenge.
Newlands then surged into a 3-1 lead, and although Rich Tolliday's goal gave Pier hope the visitors scored another couple to seal the win.
Dan Freer banged in a brace for the away side, with Tristan Mustoe also on target for Paddy Mancrief's side, with Ricky Nock their man of the match.
Seamer Sports Reserves rallied from going 2-0 down early on at Edgehill Reserves to claim a 7-2 win thanks to four goals from Danny Exley.
Liam Cooper scored after five minutes and debutant Terry Day 10 minutes later to put Edgehill in control.
Exley broke through and slotted home from a goal-kick to make it 2-1 before half-time.
Seamer came out strongly in the second half and took charge.
Exley equalised before Kris Tate blasted home from an indirect free-kick within the box.
Brad Walton curled one into top corner from outside the box to make it 4-2.
Exley added a further two and Tate another to seal the victory.
Man of the match for Seamer was Exley, with Walton and Jenson Bradbury impressive in midfield.
Andy Noon and 16-year-old Logan Atkin on his first men's game shared the man of the match award for Edgehill.
Filey Town Reserves won 3-1 at Newby, with Luqa Borg on target for the home side.
Sam Hampton was man of the match for Newby.
Jordan Padgham's double helped Goal Sports to a 5-2 win at Newlands Reserves.
Tham Dridi, Alfie Hutchinson and a Tom Corcoran penalty sealed the win for Goal Sports, Padgham being named man of the match.
Finley McGregor and Dan Hitchcock scored one goal apiece for Newlands, 16-year-old Bobby French their man of the match.
George Walmsley's brace of goals steered Westover to a 3-2 home win against West Pier Reserves.
Jack Brown also notched for Westover, with Walmsley the man of the match.