Bencic won 82 percent of her first serve points and was never broken in her Olympic debut while defeating the fast-rising American for the second time in as many meetings.
Swiss cruises in Olympic curtain-raiser
Pegula saved three break points in the opening game of the match to hold, but was having trouble making any progress on the Bencic serve. The Swiss had another break chance in the fifth game, but again the American fought it off to hold for a 3-2 lead.
In the seventh game, Pegula saved yet another break point, but a double fault on Bencic's second opportunity of the game gave the ninth seed a 4-3 lead and she closed out the set with a well-placed forehand down the line that Pegula could only net in reply.
The Swiss continued her fine play at the start of the second set, a sumptuous backhand lob for a winner giving her two break points and a backhand winner making it 2-0 to the ninth seed. She would save her first break point of the match and hold for a 3-0 advantage.
Pegula did well to stay in the match as she held and staved off a pair of break points in her next service game to remain within striking distance at 4-2. Bencic watched a match point come and go in the American's next service game before finally closing things out following a Pegula backhand error.