The West Brom frontman came off the bench to slot home an 86th-minute equaliser on a night when Ireland were second best for long periods, but, as so often under Giovanni Trapattoni, found a way to clinch a positive result.
Milan Baros had put the visitors ahead five minutes into the second half as the pressure they had created was finally made to tell. But they were unable to kill the game off and, amid late onslaught, Cox produced a cultured finish to claim a draw.
However, the degree to which the technically superior Czechs dominated possession for much of the game served as a reminder of what will lie ahead at the Euro 2012 for which they, like Ireland, have qualified.
In Bremen, France stunned Germany 2-1 with a goal in each half to win their friendly as the two sides continued their preparations for Euro 2012.
The French, who have now gone 18 games undefeated after losing the first two under coach Laurent Blanc, grabbed the leadafter 21 minutes when Olivier Giroud connected with a Mathieu Valbuena pass to beat keeper Tim Wiese.
Substitute Florent Malouda fired in from close range midway through the second half before Germany substitute Cacau cut the deficit in stoppage time.
Clint Dempsey fired the United States to a 1-0 win over Italy to leave the Azzurri’s Euro 2012 plans in further disarray. He netted 10 minutes into the second half in a largely deserved victory for Juergen Klinsmann’s visitors.