French defender Clement Lenglet gave Sevilla a deserved lead after half an hour when he headed home from a corner after the home side had crafted a number of chances in a fast start.
Spartak grew into the game and could have levelled before the break but Argentina midfielder Ever Banega doubled Sevilla's advantage with a cracking left-footed shot from outside the area on the hour mark.
Spartak pulled a goal back with 13 minutes remaining to make for a nervy finish for Eduardo Berizzo's side as striker Ze Luis converted on the rebound after Sergio Rico had parried an effort from Denis Glushakov.
Sevilla climbed above Spartak into second in Group E on seven points, two clear of the Russian side with two games remaining and one behind leaders Liverpool, who they play at the Sanchez Pizjuan later in the month.
It was a far more assured performance from Sevilla than in the humiliating 5-1 thrashing they received in the Russian capital two weeks ago, when they collapsed in the second half and shipped four goals.
Spain international Nolito came into the side at the expense of veteran winger Jesus Navas and although he was wasteful in front of goal, the former Manchester City player gave the side an extra edge in attack.
Roared on by a passionate crowd at the Sanchez Pizjuan, where they had been unbeaten in their previous 23 games in all competitions, they could have taken the lead as early as the fourth minute when Banega turned inside the area but fired wide.
Nolito then missed two chances to put Sevilla ahead before Lenglet escaped his marker to head in Banega's corner, putting the Spaniards on their way to a vital win that will restore their confidence after a nightmare display in Moscow.
(Reporting by Richard Martin; Editing by Toby Davis)
