Both sides went into the game tied on 10 points, with the Toffees having the better goal difference.
Everton started strongly, going forward at every opportunity, but failing to really trouble Gemma Jackson in the Rovers goal.
On 23 minutes, Rovers broke down the right and Amy Bland pulled the ball back to the edge of the box, where Hollie Kelsh drove a low shot past the Everton keeper, via the aid of a slight deflection.
The goal seemed to spark Rovers into life and on 32 minutes they doubled their lead. Tireless work from debutant Evie Manning paid dividends, as she closed down an Everton clearance, before directing the looping ball goalwards, past the despairing defender and goalkeeper.
Everton came flying out of the blocks at the start of the second half, as they looked for a way back into the game.
At times, Rovers struggled to get out of their own half, but kept their discipline and defended resolutely.
The arrears were reduced on 63 minutes, when Everton broke down the left and an attempted clearance from Jade Newton deflected back across goal and into the corner of her own net.
The comeback was complete 15 minutes from time when a corner from the left wasn't dealt with by the Rovers defence and an Everton forward slotted the ball home at the back post.
In the closing stages, Rovers had good spells of possession and threatened from set-plays, whilst Jackson pulled off two fine saves to secure a share of the spoils.
Manager Zac Foley said: “I cannot fault our work rate and effort and I am very proud of the players.
“We knew Everton would be a strong side and we set out a game plan to get a positive result. In the first half I thought we were magnificent and going in 2-0 up gave us a real chance. We spoke at half-time about how 2-0 was a dangerous scoreline and how we needed to continue to be disciplined as a defensive unit.
“Everton came out strongly in the second half and limited us to few chances in their half, but we stood strong and showed a great amount of character to come away with a point. There was naturally a sense of disappointment after the game because we were leading 2-0, but the girls can be very proud of the way they applied themselves throughout and the positives outweigh the negatives for sure.
“We are still unbeaten and it is a brilliant start to the season. We need to continue this type of performance level again next week against Manchester City at home.”
ROVERS: Jackson, Moorhouse, Fuller, Weston, Newton, Flynn, Farrell (Deegan 75), Kelsh, Boulton, Bland (Noori 85), Manning.
Subs not used: Lowrie.