The American made a string of impressive saves in Thursday's 4-1 victory over Wolfsburg in the UEFA Europa League, but the goalkeeper was at fault for Palace's first two goals at Goodison Park.
Romelu Lukaku had given the hosts an early lead, but Howard's foul on James McArthur allowed Mile Jedinak to equalise from the penalty spot.
The keeper's torrid day continued in the second half as he was beaten to a high ball by Fraizer Campbell, before Yannick Bolasie's calm finish increased Palace's advantage.
The visitors were forced to endure a nervy final seven minutes after Leighton Baines converted from the spot, but Palace held on to seal a 3-2 victory at Goodison Park for the second season in succession.
It was also their maiden league win of the campaign, and lifted the London club off the bottom and up to 15th in the early table.
For Roberto Martinez's men, it was a second consecutive home league defeat in what has been an inconsistent start to the 2014-15 campaign.
Neil Warnock made three alterations from the 0-0 draw with Burnley last weekend, but initially the changes failed to have the desired effect as Everton began the match in dominant fashion.
After a period of sustained possession, Everton carved out an opening for full debutant Christian Atsu in the eighth minute, but the Ghana international could only fire into the side netting after rounding Julian Speroni.
Palace's respite was only brief, however, as Leon Osman - one of four changes from Thursday - played a delicate throughball into the path of Lukaku who burst forward into space and slotted low beyond Speroni.
Osman was in the action again in the 29th minute, this time shooting too close to the goalkeeper after being teed up by Atsu.
Everton were left to rue that miss as Palace were level a minute later.
Hesitancy between John Stones, Sylvain Distin and Howard allowed McArthur to nip in, and the midfielder was sent sprawling by the keeper before Jedinak stepped up to send the resulting spot-kick into the top-right corner.
The visitors almost went ahead three minutes before the break when Bolasie's shot took a deflection off Stones and crashed back off the angle of post and crossbar.
Samuel Eto'o, making his first start for Everton, fired wide of the target in the 50th minute before another Howard error saw Palace take the lead in the 54th minute.
The 35-year-old came to collect Martin Kelly's deep cross, but misjudged the flight of the ball as Campbell rose to head into the unguarded net.
Scott Dann's block on the line denied Lukaku an equaliser on the hour and that intervention proved crucial as Bolasie gave Palace some breathing space with a composed finish after Jason Puncheon had robbed Osman.
Baines tucked home a penalty after Dann had fouled James McCarthy inside the area to set up a tense finish, but Warnock's men held on to secure the first win of his second spell at the helm despite Dann almost scoring past his own goalkeeper in stoppage time.
