Reports in Yakin's native Switzerland suggested the former Basel boss was in danger of losing his job if Spartak failed to win on Monday, but two second-half goals ensured a routine win.
Spanish midfielder Jose Manuel Jurado broke the deadlock with 63 minutes on the clock as the former Atletico Madrid man supplied an easy finish after Denis Glushakov's effort was parried by Nikolai Zabolotnyi.
The hosts eventually put the match beyond their visitors with five minutes to go, Jurado again integral as the playmaker set up Romulo, who found the net with an emphatic finish, leaving Spartak sixth in the table ahead of the league's three-month break.
Zenit go into the break with a comfortable seven-point lead at the top of the table after they thrashed visitors Krasnodar 4-0 on Saturday.
Second-half goals from Axel Witsel, Danny and Igor Smolnikov ensured an easy win after Ezequiel Garay's 12th-minute opener, denting the visitors' UEFA Champions League charge.
CSKA Moscow avoided falling further behind Andre Villas-Boas' men, though, as they won 1-0 at Kuban Krasnodar thanks to Ahmed Musa’s goal on the stroke of half-time.
Kuban failed to find a second-half equaliser, meaning CSKA stay second in the table.
Rostov end 2014 bottom of the league after losing 1-0 at home to fellow strugglers Arsenal Tula in the continuing absence of suspended manager Igor Gamula on Monday.
It was the fourth game of the Ukrainian tactician's five-match ban for derogatory comments made about the African players in his squad, with Mladan Kascelan's goal earning all three points despite Vladislav Ryzhkov's 90th-minute red card.
One of the weekend's more eye-catching result saw Dinamo Moscow thrash Amkar Perm 5-0 at home on Sunday, making up for the 0-0 draw between Terek Grozny and Lokomotiv Moscow earlier in the day.
Torpedo Moscow pulled off a two-goal comeback to draw 2-2 at home to 10-man Ufa in one Monday's early kick-offs, while Rubin Kazan simultaneously moved themselves up to seventh with a 1-0 win at Mordovia Saransk.
