The Premier League leaders fell behind in the 14th minute when Bukayo Saka netted the rebound from Kai Havertz's saved shot.
It looked as though Arsenal would take their lead into the break but a mess in defence saw them pegged back at half-time.
William Saliba appeared to bounce on Luis Diaz's mis-controlled touch but the ball went on to hit Gabriel's arm and into his own net.
Liverpool will fell lucky to have scored at such a crucial stage in the game as all three of their first-half shots were off target.
The goal could prove decisive for the Reds as they will go seven points clear at the top of the table with a comeback win.
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However, Arsenal regained the lead in the 67th minute, with Liverpool the ones to produce a defensive mishap this time around.
Virgil van Dijk did little to clear a long ball and Alisson jumped over it, allowing Gabriel Martinelli to score in an empty net.
Jurgen Klopp's side have won 19 points from losing positions this season and could be set to rescue a crucial victory once again.
The two sides met at the Emirates Stadium earlier in the year in their FA Cup third round clash, with Liverpool winning 2-0.
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They drew their reverse Premier League fixture 1-1, a match that also saw Arsenal take the lead.