Chelsea goalkeeper Cech, his country's second most-capped player behind former Manchester United midfielder Karel Poborsky (118), was delighted to reach the milestone.
"I'm only 30-years-old so 100 does not have to be the final number," he told the daily newspaper Sport before the match. "I am very proud to complete the century in an important game.
"When I was a little boy, my dream was to play at least once for the national team. And to play 100 matches? That is of course a great success. Especially when I take my age into consideration."
Udinese striker Vydra, who is on loan with England's Watford this season, opened the scoring when he headed in a cross by Jaroslav Plasil two minutes into the second half.
The 20-year-old Vydra, named this week as the English second tier's player of the season, made it 2-0 with a solo goal in the 81st minute before substitute Daniel Kolar added a late third following a centre from Tomas Hubschman.
The Czechs have eight points from five games. Armenia are second from bottom on three points.