Anzhi's Brazilian defender Joao Carlos, left unmarked near Zenit's goal, headed the visitors from the volatile North Caucasus region ahead midway through the first period.
Zyryanov equalised from close range in the 66th minute for Zenit, who were missing the league's leading scorer Alexander Kerzhakov through injury and had Portugal international Danny sent off for dissent in the second-half stoppage time.
The draw allowed CSKA Moscow, who beat last-placed Mordovia Saransk 2-1 on Sunday, to keep a two-point lead at the top of the table over Anzhi as the Russian season heads into a three-month winter break.
Russian champions Zenit are third, five points off the pace.
Monday's match was played at an empty arena after Zenit's game at Dynamo Moscow last month was abandoned when the Dynamo goalkeeper was injured by flares thrown by fans.
The Russian FA awarded Dynamo a 3-0 win, ordered Zenit to play their next two home games behind closed doors and fined each club 500,000 roubles.
Zenit were also held to a 1-1 draw by CSKA in the first match behind closed doors two weeks ago.
Russia manager Fabio Capello braved the freezing temperatures in St Petersburg to watch the match, billed as the clash between two high-profile coaches, Zenit's Luciano Spalletti and Anzhi's Guus Hiddink.
"It's very difficult to play in such a cold weather and without any spectators," said former Russia boss Hiddink.
"We played well in the first half but Zenit are a smart team and they could punish you even for a smallest mistake."
Elsewhere, Spartak Moscow went into the winter break on a high with a hard-fought 1-0 win at Rubin Kazan, ending a run of four consecutive defeats.
A 60th-minute strike by Ireland winger Aiden McGeady gave Spartak's caretaker coach Valery Karpin his first victory since he replaced ex-Valencia boss Unai Emery just over two weeks ago.
Spaniard Emery was sacked following a 5-1 home thrashing by bitter city rivals Dynamo last month.
On Monday, Karpin praised his defence, who have conceded 14 goals during that four-game sequence.
"Today, at last our defenders didn't make any glaring errors," said the former Russia international.
The win enabled Spartak to leapfrog Kazan into sixth place, 11 points behind CSKA.