Brad Lyons marked his return to Under-23s action with his first goal of the season, but it wasn't enough for all three points as Rovers missed the chance to go top of the table in Premier League
The Northern Irishman, who missed Monday's win over Brighton & Hove Albion, was back in the starting XI against Everton and gave Rovers the advantage just before half time with a delightful volley.
Rovers had their opportunities to add to the tally in the second half before a mix up at the back led to Tyler Onyango slotting home from close range late on to level things up.
It was Lyons who had the best chance to net a late winner with just a couple of minutes remaining, but he slammed wide when he really should have won the game for Billy Barr's hosts.
Rovers made four changes from the side that took to the field at the beginning of the week against Brighton down in Lancing.
Jalil Saadi, Jake Garrett, Jared Harlock and Monday's match-winner Sam Durrant all dropped to the bench following the quick turnaround of games.
Louie Annesley returned to the centre of defence, whilst a new-look midfield two saw Isaac Whitehall partner Lyons.
Connor McBride, who came off the bench to equalise in Sussex on Monday, was rewarded with a starting berth on the right of the front three.
It was an even start to the encounter, but it was Everton who had the first two opportunities early on. Ellis Sims attempted to lob Jordan Eastham after the goalkeeper's clearance reached him, before the Rovers custodian was there again soon after to deny Nathan Broadhead.
At the other end, Sam Burns looped a header wide from close range after Harry Tyrer spilt Joe Grayson's inswinging corner and McBride kept things alive.
Rovers were growing into the game thoughand Chapman saw his effort blocked by Tyrer as the game passed the half hour mark at a chilly County Ground.
However, after some sustained pressure the breakthrough did arrive with six minutes of the half remaining, and in some style. Eastham started the move from the back, and some fine passing led to Chapman's precise cross being tucked into the corner on the volley by the returning Lyons.
The Northern Irishman's strike came at the perfect time for the hosts, and meant that Barr's side went into the interval with a deserved advantage.
Einar Iversen went in search of an equaliser for Everton with 10 minutes of the second half played, but the Norwegian midfielder could only drag an effort wide of Eastham's right-hand post, with the goalkeeper's clean sheet remaining intact.
Although he had nothing to do with Iversen's attempt, Eastham had to be alert a few moments later, diving to his right to beat away Broadhead's rasping drive after the winger cut in from the left flank.
Time was running out for the Toffees to get anything from the game, but a bit of fortune for David Unsworth's side led to the equaliser coming through a mistake at the back for Rovers.
After a high punt forward, it looked like Joe Grayson had it under control, but the captain's attempted pass back saw Eastham in no man's land, and the lack of communication was exploited by Oyango, who slipped into an empy net with only six minutes remaining.
The visitors' tails were up at this point, and substitute Rhys Hughes slammed wide as the Toffees went in search of a late winner.
The game was end-to-end as both teams went for broke, and Lyons missed a glorious chance to complete his brace and put Rovers back in charge when he fired wide after Lewis Thompson picked him out in the box.
Despite the frantic end in Leyland, the draw was probably the fairest outcome as both sides went away with a point apiece.
Rovers return to action on Monday 7th November, with Tottenham Hotspur the visitors to the County Ground, kick-off 7pm.
Rovers: Eastham, Pike, Barnes, Annesley, Grayson (c), Thompson (Garrett, 90), Whitehall, Lyons, McBride, Burns, Chapman (Durrant, 90).
Unused substitutes: Stergiakis, Saadi, Harlock.
Goal: Lyons, 39.
Everton Under-23s: Tyrer, Pennington, Small, Baningime (c), Astley, Branthwaite, Kouyate (Jagne, 62), Iversen (Hughes, 62), Simms, Onyango, Broadhead.
Unused substitutes: Hansen, Ouzounidis, Anderson.
Goal: Onyango, 84.
Booked: Onyango, 8, Pennington, 47.
Referee: Scott Simpson.