On 70 minutes Sverkos slotted in a low volley from 12 yards after latching on to a ball over the top of the defence.
The Swiss were denied an equaliser when Johan Vonlanthen's volley hit the bar.
And it might prove that the width of the woodwork could be the end of the Swiss, with tough matches against Portugal and Turkey to come in Group A.
Czech Republic coach Karel Bruckner conceded his side were "not at their best".
"We did a good job. The first match is always very important and three points is an excellent start," he said.
"We were not at our best but we can play better and we will play better.
"I don't think it is fair to say we set out to play a defensive game. We were against the home side and who were a goal down for half of the second half."
He added: "We were always going to come under pressure and although we made a few mistakes, we coped well."