Hannah Cain opened the scoring just before the break, before Annabel Blanchard's converted penalty put the game level heading towards 90 minutes before both sides netted in injury-time.
Shannon O'Brien thought she had scored a 94th-minute winner with a top-corner finish from close range but Abbie Larkin connected with a low cross four minutes later to pull the hosts back for the second time in the game.
With one game to go, and two points behind a potential highest-ever points tally in the Barclays Women's Super League, all eyes will turn to our season finale against West Ham United next Saturday afternoon at King Power Stadium (12:30pm BST kick-off). Cain breaks the deadlock
Hannah Cain broke the deadlock in Sutton.
Having weathered the storm that Crystal Palace were brewing for large parts of the first half near the Leicester box, we managed to take the lead just before the referee's whistle through Cain.
After the ball fell kindly to Janice Cayman in the box, the experienced Belgian international squared it to the striker, who turned it goalwards, out of reach of Shae Yanez.
The Eagles hit back
Battling against the Eagles.
With less than 20 minutes remaining on the clock, the hosts equalised from 12 yards after former Fox Josie Green was fouled in the box by Courtney Nevin.
Up stepped Annabel Blanchard, also a former Leicester player, who sent Janina Leitzig the wrong way to find the right hand side of the net to level things back up again.
Late drama in Sutton
Shannon O'Brien found the net in injury time.
As the fourth official indicated an additional 10 minutes of added time, both teams felt the possibility of getting something further out of the game, with Leicester hitting the first blow.
Four minutes in, O'Brien, who looked determined to score since her introduction, found the ball at her feet inside the box and calmly found the top corner to spark celebrations in the away end.
But with so long still left to play, Palace knew they weren't out of it yet, and equalised late on, in the 98th minute, when Larkin pounced on a low cross into the box.
Elation followed by quick heartbreak means that Leicester remain one point below their best-ever tally as the campaign concludes on Filbert Way next weekend.