Frank Lampard put Chelsea ahead in the 56th minute at the Mestalla but his fine goal was cancelled out when Ivory Coast forward Kalou, who had replaced Lampard only minutes earlier, flapped an arm at a Valencia cross and the referee pointed to the spot.
Striker Roberto Soldado struck the ball low to goalkeeper Petr Cech's left for an 87th-minute leveller before Alves produced the last of a string of brilliant stops to deny substitute Nicolas Anelka.
The Brazilian had earlier saved twice from Fernando Torres and once from Ramires during a frenetic period of Chelsea pressure that culminated in Lampard's goal.
"We had chances to make it 2-0 in the second half but we had bad luck," Chelsea manager Andre Villas-Boas said at a news conference.
Asked about the Kalou incident, the Portuguese added: "We don't praise people in public and we don't criticise either. It was one of those incidents you can't control."
The home side's French defender Adil Rami had to be alert to thwart Torres in the third minute when the Spain striker raced through the middle following an error by David Albelda.
Lampard forced a fine save from Alves with a powerful low free-kick in the 14th before Valencia had their first real chance in the 25th when Pablo Hernandez turned Jordi Alba's cross into the side-netting.
"Lampard put in a fine individual performance and he scored a goal," Villas-Boas said. "He is a great player and we are very pleased with him."
