Markram struck 89 not out from 47 deliveries while Lhuan-dre Pretorius hit 44 in an opening stand of 83 as the hosts chased down a target of 174 to win with 13 balls to spare.
The Windies were sent in to bat first at the toss and were restricted to a total of 173-7 with Shimron Hetmyer hitting the top-score of 48 from 32 balls.
The signs looked ominous when Brandon King dispatched Kagiso Rabada for fours off the first two balls of the match.
King though was undone by Corbin Bosch for 27 before Proteas spinner George Linde ran through the middle-order to finish with figures of 3-25 in his four overs.
Linde took the scalps of stand-in Windies captain Chase and then got rid of Hetmyer in the final over as the tourists looked to the 190-run mark.
Chase contributed 22 while Rovman Powell was unbeaten on 29 when the innings came to a close but the feeling was that the Boland Park pitch was a good one to bat on.
Markram and Pretorius then made the target seem like a cake walk as the Proteas got off to a quick-start with the left-handed Pretorius getting his runs off just 28 balls.
The opening partnership of 83 took just 7.5 overs before Pretorius was dismissed by the off-spin of Chase going for another boundary.
The home skipper then found good support for Ryan Rickelton, in his new role at number three, with the left-hander eventually ending on from an unbeaten 40 as the Proteas coasted to victory.
The hosts will have a chance to wrap up the three-match with the second game taking place in Centurion on Thursday.
West Indies captain Shai Hope knows first hand about that danger that Proteas batter Dewald Brevis will pose to his team in the three-match T20I series that kicks off in Paarl on Tuesday.
Proteas captain Aiden Markram is pleased that most his team has found form ahead of the three-match series against West Indies, starting in Paarl on Tuesday, and the T20 World Cup.
Alzarri Joseph has missed out on West Indies' T20 World Cup squad due to injury while Quentin Sampson was named in the 15-man group for the tournament that will be co-hosted in India and Sri Lanka.
Tony de Zorzi and Donovan Ferreira have been ruled out of the T20 World Cup due to injury, resulting in Ryan Rickelton and Tristan Stubbs being called up to the Proteas squad.
