Edinson Cavani completed the win with an acrobatic effort before halftime as the impressive South Americans sounded a warning to World Cup group opponents Egypt, Russia and Saudi Arabia.
Suarez showed typical cunning as he won the penalty in the 10th minute, tumbling over the outstretched leg of goalkeeper Jiri Pavlenka as he chased a ball that was going away from the goal and posed no real danger to the Czech defence.
The 31-year-old, making his 96th appearance, fired the spot kick into the roof of the net.
With Suarez and Cavani proving a handful for the Czech defence, it was no surprise when the two-times world champions went further ahead in the 37th minute.
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Nahitan Nandez headed the ball into the Czech area where Cavani, with his back to goal, produced a memorable scissors kick to fire past Pavlenka.
(Writing by Brian Homewood in Berne; editing by John Stonestreet)
