The former Boys Town and Charleroi striker got goals in the 20th, 62nd and 86th minutes to help Spartak advance.
Dutch international Quincy Promes also got two goals in the 6th and 17th minutes while Swedish striker Jordan Larsson, son of former Manchester United and Barcelona forward Henrik Larsson, got the other goal in the 83rd minute.
Spartak Moscow is 13-time winners of the Russian Cup, with their last triumph coming in the 2002-03 season.
The 24-year-old forward recently secured a move to Russian Premier League club Spartak Moscow after spending two years at Belgian club Charleroi. The move will represent a step up for the Jamaican player, with the Russian club routinely taking part in Europe’s top competitions.
Football in Russia has, however, been plagued by controversy in recent years with fans often known to direct racist and xenophobic chants towards players of different races who represent various clubs. The issue had become so prominent in recent years that there was a campaign to address the issue ahead of the country's hosting of the 2016 World Cup.
However, according to Nicholson’s agent Kevin Cowan. Issues pertaining to racism impact players everywhere.
"There is racism everywhere," Cowan told Voetbalkrant.com.
“That shouldn't be a factor. Shouldn't all players be playing in Italy or Russia otherwise?"
"Spartak came and wanted Shamar, then we are not concerned with possible racism. In the long run, he wants to go to an absolute top competition, but this is a nice step and a very nice club."
The ongoing invasion of Ukraine by Russia, which has sparked global condemnation, prompted the European football governing body to reschedule all the club’s matches for neutral venues, following an emergency meeting on Friday. The ruling applies to all Russian and Ukrainian teams in European competitions.
Spartak Moscow has been drawn to face RB Leipzig in the round of 16, with the tie commencing at the Red Bull Arena in Germany, on March 10. The return leg will take place the following week, but the venue is yet to be announced.
"The UEFA Executive Committee also decided that Russian and Ukrainian clubs and national teams competing in UEFA competitions will be required to play their home matches at neutral venues until further notice,” a release issued from the sport’s governing body explained.
Nicholson joined the Moscow club from Belgian Pro League side RSC Charleroi, where he scored 13 goals and five assists in 18 matches last year.
