Marco Streller, scorer of the first goal in the 2-1 win over United which took Basel into the Champions League last 16 at the English side's expense, gave Basel the lead in the 77th minute at the Maladiere.
But Neuchatel, where controversial Russian owner Bulat Chagaev has fired four coaches and the administrative staff since taking over the club in May, levelled through Abdou Dampha four minutes later.
The hosts played most of the second half with 10 men after Stephane Besle was sent off for a second yellow card.
Basel, attempting to win the Swiss league for the third season in a row, reached the halfway mark of the season top of the table with a seven-point lead over FC Lucerne and Sion.
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