Flying winger Zaha injured his right knee during the opening-day defeat to Huddersfield Town and has been powerless as Palace lost their opening seven league matches without scoring a goal.
Another defeat to nil would have set an unwanted English league record at nine, including one at the end of last season, but Selhurst Park erupted early on when an Andros Townsend cross crept past Thibaut Courtois via a combination of Yohan Cabaye and Cesar Azpilicueta.
Tiemoue Bakayoko was given the freedom of the Palace area to head home his first Premier League goal and level the scores, but the influential Zaha – who was a menace throughout – restored Palace's lead shortly before the break with a cool finish.
An inevitable second-half barrage arrived from Chelsea and Cesc Fabregas lashed an effort against the crossbar, but Palace clung on for a priceless victory.
It marks another disappointment for Antonio Conte, whose side were beaten 1-0 at home by Manchester City last time out and the Blues now trail Pep Guardiola's league leaders by nine points.
Palace remain bottom of the table, seven points adrift of 17th, but the return of Zaha will give Roy Hodgson – who tasted victory as Palace boss for the first time – renewed optimism.
Zaha provided Palace with fresh attacking impetus and he forced Courtois into an early save after collecting Townsend's low left-wing cross and turning Gary Cahill in the area.
The wait for a goal was over in the 11th minute. James McArthur cleverly slipped a pass to Townsend, whose drilled cross ricocheted off Cabaye's knee under a challenge from David Luiz and clipped Azpilicueta before squirming past Courtois.
Palace's frailties were exposed with startling ease just seven minutes later, though, as Cesc Fabregas fired in a corner from the right that Bakayoko headed in unmarked for his first Premier League goal.
Zaha lashed an effort past the left post, while more poor marking at a corner led to Michy Batshuayi – deputising for the injured Alvaro Morata in one of four Chelsea changes – heading wastefully over the crossbar.
Chelsea then lost Victor Moses to a hamstring injury before their misery increased on the stroke of half-time.
Mamadou Sakho powered deep into Chelsea's half and fed Zaha, who brilliantly jinked inside Azpilicueta before placing his shot across Courtois into the bottom-right corner.
Chelsea upped the tempo early in the second half and Fabregas' stinging 25-yard drive beat veteran goalkeeper Julian Speroni – playing in place of the injured Wayne Hennessey – but rattled the bar.
The visitors continued to create the better second-half chances and Marcos Alonso looped a header over from Willian's corner just after the hour before Pedro's long-distance drive was saved by Speroni.
Palace should have put the game to bed in the closing stages when Courtois spilled Townsend's 25-yard effort, but Patrick van Aanholt somehow drilled wide on the follow up with the goal gaping.
It almost proved a costly miss as Sakho recklessly tried to backheel out of danger against Charly Musonda, but thankfully for a raucous home crowd Fabregas drilled wide.
Key Opta stats:
- Palace’s 11th-minute goal meant they ended a run of 640 minutes without scoring from the start of the season. Indeed, in Football League history - only Halifax Town in the fourth tier in 1990-91 (730 minutes) had a longer wait to score.
- Chelsea have lost successive league games against the Eagles for the first time since March 1982, although there were nine years between both meetings.
- Roy Hodgson is one of two managers to win against Chelsea with four different Premier League clubs (Blackburn, Crystal Palace, Liverpool, West Brom) – the other being Sam Allardyce.
- Antonio Conte has lost three of his first eight league games in a campaign for the first time since 2009-10 when taking over at Atalanta (in September 2009) in Serie A (also three losses).
- Chelsea have lost consecutive Premier League games under Antonio Conte for just the second time (also September 2016).
- This is just the sixth time that the team starting the day bottom of the Premier League have beaten the reigning champions.