Cisse, who scored at the death against Stoke on Sunday, headed the only goal of the tie in the 94th minute of the second leg to send the Magpies into the quarter-finals.
"Marvellous finish," Pardew said on ESPN. "Papiss did it on Sunday and did it again tonight [Thursday].
"It was a quality cross and he finished it off."
Newcastle looked shaky before the break, but their opponents had Mehdi Carcela-Gonzalez sent off 10 minutes after the break and the hosts took advantage.
Pardew added: "We did a lot better in the second half and put them under pressure and when you put them under pressure something gives.
"I think we've put out one of the best teams in the competition if I'm honest.
"We just squeezed over the line and I'm highly delighted. We've had a very, very tough two games."
Defender Steven Taylor described the win as "massive".
"In the first half we got the runaround a bit, but in the second half we got stuck in and we did it," he said.
"Papiss has stepped up to the plate and scored and got us through to the quarter-finals. It was magnificent."
Anzhi boss Guus Hiddink felt his side created enough early chances to win the game.
"We created, against a Premier League team, four or five open chances. We can blame ourselves (for missing them)," the Dutchman said.
He also described the red card as "harsh".
"It was not a wise action what he did, but it was harsh," he said. "The referee was maybe a little bit influenced by the crowd."