The West Brom frontman came off the bench at the Aviva Stadium on Wednesday night 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.
Trapattoni very much had Poland and Ukraine in mind when he selected his strongest available starting line-up, and his critics among a crowd of 37,741 will hardly have been appeased by his decision to hand exciting Sunderland winger James McClean just the final 11 minutes and leave Everton defender Shane Duffy sitting on the bench.
To the surprise of few, the Italian had decided to stick to his tried and tested personnel and method in his team's final friendly before they meet up in May and begin in earnest their preparations for the summer.
Predictably, the pattern of the first half followed that of many of Ireland's games under his tenure as his hard-working and committed players remained organised in the face of a determined onslaught and took a direct approach to their own efforts to open the scoring.
The 72-year-old's one concession after running the rule of Group C opponents Croatia, Spain and Italy, was to ask skipper Robbie Keane to play in, as he called it, a "Francesco Totti role" behind striker Shane Long.
Ireland nearly got off to the perfect start when, with less than a minute of the clock, Aiden McGeady skipped past right-back Theodor Gebreselassie and crossed to the far post, where Long rose well and made good contact, but directed his header straight at Czech skipper Petr Cech.
However, opposite number Shay Given was in action at the other end within two minutes when Jiri Stajner played a neat one-two with Baros and drilled in a shot which the keeper blocked with his legs.
Where the Czechs passed the ball confidently and patiently waited for the gaps in the Irish defence to open up, the home side defended tigerishly, but almost caught the visitors flat-footed with 15 minutes gone.
Keane expertly plucked Keith Andrews' long ball out of the air and as Cech raced from his line, attempted to poke it past him, only to see the keeper make a vital block.
Right-back John O'Shea glanced a header just wide from McGeady's 20th-minute free-kick, but as the half wore on and Jaroslav Plasil and Petr Jiracek started to orchestrate in the middle of the field, it was the visitors who began to increase the pressure.
But for all the possession, Ireland remained resolute, and it was not until the final minute of the half that Given, who had earlier escaped unpunished after allowing Stajner to charge down his attempted clearance, was called upon once again.
This time, it was Jan Rezek who cut inside from the left to send in a curling effort which the Aston Villa man had to get down well to turn away to ensure the sides remained locked together at the break.
Ireland were guilty of allowing Milan Petrzela far too much space with 50 minutes gone, and were relieved when he failed to make the most of it by picking out Baros inside the penalty area, although the respite was temporary.
Rezek picked up possession in an equally promising position seconds later and cleverly switched the play to find the unmarked Baros, who drew Given before lifting the ball over him and into the net.
Ireland might have been level within seven minutes after Long picked out Damien Duff on the edge of the penalty area with an intelligent cross, but the Fulham winger wastefully curled his effort high and wide.
He was almost made to pay instantly when Rezek dispatched a well-struck shot which only just missed the target with Given at full stretch.
Trapattoni opted for change with 27 minutes left, but to introduce Paul Green and Stephen Hunt - not young pretenders Duffy and McClean, who remained seated on the bench eight minutes later when Cox and Jonathan Walters replaced Keane and Long.
With fresh legs aiding a concerted fightback, the home side got themselves back into the game with just four minutes remaining when Cox ran onto Andrews' pass, cut inside defender Tomas Sivok and side-footed the ball past Cech from an improbable angle to snatch a draw.