Neil Critchley's team looked set to follow up a draw with Manchester United and a convincing win over Blackburn Rovers with another three points when substitute Okera Simmonds fired in five minutes from time.
But Joe Powell's late, late penalty ensured a hard-fought contest at Kirkby ended honours even.
The visitors started the game the brighter of the two teams, with Jamahl Hector-Ingram providing an early test for Dan Atherton, sending a firm shot to the goalkeeper's near post after being found by a ball over the top.
That chance served as something of a wake-up call for the Reds, though, and they responded to create two half-chances of their own by way of response.