Uzbek sixth seed Istomin, in his first tournament since Wimbledon, proved far too good for American lucky loser Rajeev Ram 6-1 6-4.
In a dominant 68-minute performance on the hard courts at the ATP 250 event, Istomin sent down eight aces and broke serve three times.
Istomin faces Lukas Lacko in the second round after the Slovakian claimed a 6-2 7-5 win over American wildcard Nathan Pasha.
Also in his first appearance since the third gram slam of the year, Matosevic thrashed the Dominican Republic's Victor Estrella Burgos 6-0 6-2.
The Australian eighth seed needed just 43 minutes to advance against the veteran world number 82, who reached the semi-finals in Bogota last week.
Awaiting Matosevic in the second round is Jack Sock after the American eased past Colombian Alejandro Gonzalez 6-2 6-4.
Ukraine's Sergiy Stakhovsky was unable to continue his good form, beaten 7-6 (7-3) 3-6 6-0 by American wildcard Robby Ginepri.
Stakhovsky, who claimed a Challenger Tour title in Binghamton last week, could only win 10 points in the deciding set against the two-time champion.
Ginepri will face top seed and defending champion John Isner in the second round.
In an all-American affair, Tim Smyczek crushed Ryan Harrison 6-0 6-2.
Ukraine's Illya Marchenko advanced with a 6-4 6-4 win over fellow qualifier John-Patrick Smith of Australia.
German Benjamin Becker was a 6-4 6-2 victor against out-of-form Australian Matthew Ebden.
Dutch lucky loser Thiemo de Bakker served 10 aces in his 6-1 6-2 thrashing of Canadian qualifier Steven Diez.