The Reds' woes against the lower-ranked teams continued as they squandered the lead, having broken the deadlock with a superb free-kick from Philippe Coutinho midway through the first half.
Benteke levelled matters three minutes before the break and was presented with an easy header to complete the comeback win on 74 minutes, handing Sam Allardyce his first taste of success at Anfield in 12 league visits.
Palace did well to contain the hosts in the opening quarter of the match, and former Red Benteke had a great chance to open the scoring against his former club on 21 minutes.
The striker showed good footwork to go past Lucas before advancing on goal and curling the ball beyond Simon Mignolet and the right post.
But Allardyce's men gave away a free-kick in a dangerous position three minutes later and were made to pay. Coutinho conjured up a special goal as he whipped the ball over the wall and beat Wayne Hennessey at his near post from 25 yards out.
The Reds continued to probe but they found Palace well organised in defence, although James Milner penetrated the back-four in the 39th minute with a reverse pass on the left to release Georginio Wijnaldum, who cut the ball back for Emre Can, only for the German to horribly miscue his side-footed effort from 12 yards out.
However, the visitors hit back just before half-time as Joel Ward played in Yohan Cabaye on the right with a long ball and the Frenchman's quality cross was tapped home at the back post by Benteke to equalise in front of the Kop.
The Belgium international threatened again in stoppage time, chesting down an inswinging cross from Jason Puncheon on the right, but his volley lacked the power to beat Mignolet.
Liverpool made a good start to the second half and Coutinho should have done better on 50 minutes when he displayed quick feet to out-fox James Tomkins with a sharp turn before firing over from just outside the area.
The Brazilian went close again moments later as he was allowed to get into the box and rode one challenge before seeing his shot blocked by Tomkins.
Lucas then blazed over from 17 yards out after a corner was only half-cleared into his path, while compatriot Coutinho had a deflected header from Nathaniel Clyne's cross comfortably saved by Wayne Hennessey on 56 minutes.
The home fans became restless as their team struggled to turn possession into chances, although Roberto Firmino had them out of their seats on 65 minutes with a driven effort that flew wide of the left post, after Wijnaldum had played him in on the right.
The Eagles weren't just sitting back, though, and Cabaye fashioned a good opportunity for himself on 71 minutes with a swivel and turn to shoot over from eight yards out, after the ball had pinged around inside the box.
They would go in front three minutes later following a mistake from Firmino, who failed to deal with Puncheon's corner at the near post which saw Benteke head home from six yards out.
The Merseysiders went in search of an equaliser in the final 16 minutes, but Palace held firm at the back to pick up a third successive win at Anfield.