Pools had to come from behind after Joe Kizzi headed the visitors in front inside three minutes at the Suit Direct Stadium.
But Lee's side levelled in the second half when Tom Crawford got on the end of Zaine Francis-Angol’s cross to lift into the roof of the net with neither side able to find a winner.
And here is how Pools were rated against Sutton.
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1. Ben Killip - 6
Largely untroubled throughout the game. Was rooted for the opener. Picture by FRANK REID Photo: Frank Reid
2. Reagan Ogle - 6
Important challenge to deny Bugiel in the first half. Did ok in place of Sterry. (Credit: Will Matthews | MI News) Photo: Will Matthews
3. Neill Byrne - 7
Solid display with a key interception to deny Wilson. (Credit: Mark Fletcher) Photo: Mark Fletcher
4. Timi Odusina - 6
A couple of mistimed clearances in the second half but another strong shift. (Credit: Will Matthews | MI News) Photo: Will Matthews