Barcelona full-back Daniel Alves opened the scoring in the 16th minute and Messi added two more in the space of 12 minutes before half-time with his 79th and 80th goals during this calendar year.
The Spaniards, who have also secured top spot in Group G after shrugging off the 2-1 defeat at Celtic this month, controlled the tempo with their famous tiki-taka passing game on Moscow's slick artificial turf and often picked holes in Spartak's porous defence.
"We couldn't allow what happened at Celtic to happen again," Messi told Spanish TV.
"We knew we had to come out strongly right from the start because it's always tough to play away in this competition and even more so given the state of the pitch.
"Obviously the fact we didn't concede is a boost for everyone, especially when we have been letting in too many goals recently."
Brazil international Alves beat Spartak goalkeeper Andriy Dykan with a low blast from outside the box after the Russians failed to clear the ball following Barcelona's build-up near the goal.
Messi has also now netted 56 goals in Europe's elite club competition, moving him level with Ruud van Nistelrooy into second place on the Champions League's all-time top scorer list. Only former Real Madrid striker Raul has scored more (71).
Messi also scored twice at the Nou Camp to power the Catalan club to a comeback 3-2 win over Spartak in the group's opening fixture two months ago.
Most of the 70,000 fans, who braved the cold to fill the Luzhniki Stadium, came to see Messi and they got their money's worth.
Cesc Fabregas, Andreas Iniesta and Pedro also missed good chances to add to Barca's total.
