It was an end-to-end opening as Charlie Devlin's free-kick found Ashleigh Plumptre at the back post but her flicked effort was held by Megan Borthwick, while Sarah Robson headed wide from an early Durham corner.
The ball then fell kindly for Sarah Wilson to strike from the edge of the area, with her half-volley narrowly missing the top of the crossbar.
The Durham captain again found space for a shot, this time seeing her low strike blocked, before Hepple's strike from range was comfortably saved by Levell, as the visitors started to get a hold on the game.
And that pressure paid off when Roberts volleyed into the roof of the net on 19 minutes, after City initially failed to clear Nicki Gears' cross.
Leicester tried to respond through Devlin, who struck wide, and Bailey-Gayle, who saw her attempt pounced on by Borthwick after getting on the end of Esmee De Graaf's cross.
Durham substitute Lauren Briggs then capitalised on a stray pass from the backline, winning back possession and striking over the bar near the end of the first-half.
After a double change at the break, City had fresh impetus and were back on level terms within six minutes as Allen managed to guide the ball over Borthwick with an inch perfect lob from just inside the area.
Bailey-Gayle then went close to completing the turnaround, cutting inside onto her right foot and firing just over the bar.
But just as Leicester were getting on top, Durham struck again, on 66 minutes, via Hepple's superb free-kick, which sailed straight into the top corner from 25 yards out.
City looked to show their powers of recovery again and Millie Farrow saw her effort fail to hit the target after a scramble in the Durham area.
Paul then tried to make an immediate impact from the bench but found Borthwick equal to her effort and the away side looked to have thwarted City's late attempts to equalise for the second time.
However, with 92 minutes on the clock, Paul, who had gone close earlier, managed to find the net emphatically with what was virtually the final opportunity of the game.
Lachante Paul celebrates with her teammates after firing in City's late leveller.
Leicester looked to be heading for a first defeat of the league season until Lachante Paul, on as a substitute with 15 minutes remaining, fired home a sweetly struck volley to earn City a hard-fought point.
Captain Remi Allen was impressive in the middle of the park, scoring City's first goal.
Captain Remi Allen cut a composed figure in the middle of midfield, breaking up the opposition's play and driving forwards when possible. She got the Foxes back on level terms soon after the break and epitomised the fighting spirit that Leicester had to show in order to get back into the game.
Where does it leave us?
Paige Bailey-Gayle drives forward for the Foxes.
City are fifth in the Championship table, with five points from the opening three games.
Esmee De Graaf
Esmee De Graaf battles for possession in midfield.
Next up, the Foxes host Liverpool in the league at Farley Way Stadium on Sunday 11 October (2pm BST kick-off).
City: Levell; De Graaf (Everett 77), Howard, Tierney, Plumptre; Allen (C), Barker, Bailey-Gayle, Devlin (Thomas 45); Flint (Littlejohn 45), Farrow (Paul 77).
Subs not used: Lambourne, Cataldo, Smith, Fergusson.
Goals: Allen 51', Paul 90+2'
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