Chechen side Terek were forced to host Zenit at Anzhi's arena in neighbouring Northern Caucasus region of Dagestan because their ground was banned after Chechnya's strongman leader Ramzan Kadyrov insulted a referee over a loudspeaker in their previous home game against Rubin Kazan.
With Kadyrov's blessing, Terek ordered 400 buses to take several thousand die-hard supporters on a 165-km trip to Makhachkala but the fans were left hugely disappointed as their team lost for the third time in four matches and had a player sent off for a second successive game.
Belgium international Axel Witsel headed Zenit ahead after eight minutes and Portugal fullback Bruno Alves doubled the lead following a fine run into Terek's box early in the second half.
Substitute Konstantin Zyryanov added a third in stoppage time to complete the scoring for the visitors for whom Alexander Kerzhakov missed a penalty in the first half.
The win moved Zenit into second place, five points behind CSKA Moscow, who visit bottom team Alania Vladikavkaz on Monday, as Anzhi dropped to third, seven points off the lead with eight matches remaining.
In Krasnodar, under-strength Anzhi suffered their heaviest defeat of the season with Brazilian striker Vanderson scoring a hat-trick for the home team.
Vanderson, Krasnodar's leading scorer with 11 goals this season, opened the scoring in the 34th minute and, after compatriot Joaozinho made it 2-0 shortly after the break, added two more in the 59th and 89th minutes to complete the rout.
"What can I say, 4-0 against a team like Anzhi - I can't be too disappointed," Krasnodar's Serbian coach Slavoljub Muslin told Russian television NTV Plus.
"But we were a bit lucky - they missed two good chances when the score was 0-0. Besides our keeper (Alexander Filtsov) had a great game."
Anzhi were missing several leading players through injury, including captain Samuel Eto'o, Brazilian playmaker Willian and Russia international Yuri Zhirkov, but coach Guus Hiddink refused to look for excuses.
"Today we were given a good lesson on how to take your chances. We missed ours while they didn't," said the Dutchman.
In the late game at Moscow's Luzhniki stadium, Spartak were held to a 2-2 draw by Kuban Krasnodar, dropping to seventh, 12 points off the pace.