The Green and White Army had an early chance when Josh Magennis put a header wide within the first three minutes of kickoff, but the Czechs also had some joy in attack.
Some one-touch football ended with Michal Krmencik trying to get on the end of a pass in the middle of the box, but he was flagged marginally offside.
The breakthrough was made against the run of play just shy of the half-hour mark when Evans helped along Oliver Norwood's powerful header towards the back post after Brunt's corner was initially cleared.
Evans, who was linked with a move to Manchester City in the summer, celebrated his first goal for his country since March 2009, and the jubilant atmosphere continued when Brunt doubled Northern Ireland's lead by curling the ball into the bottom corner from a free kick.
Czech Republic dominated the ball, but they were unable to make the most of their opportunities, one of which resulted in Krmencik failing to get on the end of Josef Husbauer's teasing cross.
Northern Ireland spent the majority of the final 20 minutes of the game defending, but they were able to hold off a comeback from their opponents.