The visitors had taken the lead five minutes into the second half through former Liverpool and Aston Villa striker Milan Baros. And they looked to be on course to beat an Ireland side who, like them, have also qualified for the UEFA EURO 2012 finals in Poland and Ukraine. But Cox, a striker with English Premier League side West Bromwich Albion, came off the bench to level four minutes from time.
For much of the match the Czechs were clearly technically superior and an Republic of Ireland side coached by Giovanni Trapattoni struggled for possession. However, as so often is the case under the 72-year-old Italian manager, Republic found a way to emerge with a creditable result and extend their unbeaten run to 12 games.
"We needed to go a goal behind to wake us up," Sunderland and Ireland defender John O'Shea told the BBC. "It's something we need to improve upon. We can't afford to give teams a goal start. We were a little bit flat."
Shane Long and Robbie Keane were denied by Petr Cech early on, but Czech Republic regrouped to dominate the remainder of the first half. Ireland could have been ahead inside a minute, but Long headed straight at Cech following a cross from Aiden McGeady. However, Jiri Stajner then forced Shay Given into a fine save after exchanging passes with Baros.
Los Angeles Galaxy forward Keane then saw his shot from the edge of the box saved by Cech and the lively opening exchanges continued when O'Shea's glancing header from McGeady's free-kick drifted just wide of the post.
However, Czech playmakers Jaroslav Plasil and Petr Jiracek gradually exerted their influence in an impressive display of possession football and a minute before half-time Given got down well to turn away Jan Rezek's dipping shot.
Rezek, however, did play a key role in the opening goal, drawing in three defenders as he collected the ball on the edge of the penalty area and then releasing Baros with a reverse pass before the striker shot over Given. And in the 58th minute Rezek nearly made it 2-0, with his curling effort narrowly off target.
Four minutes from time Czech Republic were made to pay for their failure to score a second goal when Cox beat Cech from a tight angle, shooting through the keeper's legs at the near post after Keith Andrews had won the ball.