The holders and winners for the past two seasons appeared to be heading for a fourth-round exit at Everton after falling behind to a Louis Saha header.
But Kalou, who had entered the field just five minutes earlier, booked a replay at Stamford Bridge as he finished off a swift counter-attack 15 minutes from time.
It came just moments after Petr Cech had produced a brilliant save to prevent Seamus Coleman doubling the Toffees' lead.
Both sides went close to a late winner as Ramires struck a post for Chelsea and Jermaine Beckford also tested Cech.
Source: PA
Source: PA