Raonic, from Thornhill, Ont., beat Griekspoor 7-6, 6-3, 6-4, for his second win of the five-match tie.
Denis Shapovalov of Richmond Hill, Ont., won his singles rubber on Friday night, while Toronto's Daniel Nestor and Vancouver's Vasek Pospisil lost their doubles rubber on Saturday.
Griekspoor was subbed in for No. 44 Robin Haase an hour before the match. The 27-year-old was making his Davis Cup debut and is ranked 224th on the ATP Tour. He peaked at No. 205 in the world on Aug. 6.
Haase lost a lengthy five-set match to Shapovalov on Friday night, while Raonic had a brief three-set win over Thiemo de Bakker earlier that night, making him better rested.
Raonic, No. 20 on the ATP Tour, was the highest-ranked player in the tie.
Despite being a lopsided matchup on paper, Griekspoor came out strong, taking a 3-1 lead in the first set. Raonic leaned more and more on his big serve, firing nine aces to Griekspoor's one to battle back and take the set.
Raonic took firm control of the match in the second set. He added six more aces and finished off the frame when Griekspoor's volley return went wide.
He put away the third set with back-to-back aces. Raonic finished with 23 aces to Griekspoor's five.
The 46-year-old Nestor was honoured in a pre-match ceremony where he was inducted into Canada's Tennis Hall of Fame.
Nestor's skill in doubles competition made him invaluable to Canada at the Davis Cup, as he competed in 53 ties over 25 years, a reliable doubles competitor who earned a team-best 33-13 doubles record and was 15-15 in singles rubbers.
Nestor won eight Grand Slam doubles titles over his lengthy ATP Tour career with a variety of partners and won gold for Canada at the 2000 Sydney Olympics with Sebastien Lareau. He and Vasek Pospisil finished fourth in the 2016 Rio Games. In 2002, Nestor peaked as the top doubles player in the world.
