Cisse scored at the death in the Premier League against Stoke on Sunday and showed impeccable timing again to head home Sylvain Marveaux's cross in what was the only goal of the two-legged tie.
Newcastle probed in vain against 10 men for most of the second half, Mehdi Carcela-Gonzalez sent off (55) for two yellow cards in quick succession, but Pardew insisted his side had come up against one of the competition's best.
"It was a marvellous, marvellous finish," Pardew said of Cisse's late intervention.
"Papiss did it on Sunday and he did it again tonight. It was a quality cross and he finished it off.
"We did a lot better second half, put them under a lot of pressure and if you put teams under pressure, something gives.
"They had the guy sent off and it was a question of were we going to get the goal in the 90 minutes or in extra-time; luckily we got it with the last kick of the game.
"They are a top, top team. They didn't let us have a moment's peace and they're fantastic on the ball.
"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."
Anzhi boss Guus Hiddink felt his side created enough early chances to win the game - and took issue with his player's dismissal.
"We created, against a Premier League team, four or five open chances. We can blame ourselves (for missing them)," the Dutchman said.
"It was not a wise action what he did, but it was harsh. The referee was maybe a little bit influenced by the crowd."