The Czechs, who will fancy their chances in the finals with a group containing Russia, Greece and co-hosts Poland, were the far more dangerous side and will feel hard done by that striker Milan Baros' 40th international goal was not enough for victory.
Facing a far tougher task this summer with Spain, Italy and Croatia between them and a quarter-final place, Ireland carved out the better early opportunities but strikers Robbie Keane and Shane Long were unable to make the most of a half chance each.
The visitors' best chance of the first period fell to Jan Rezek who was denied by a fine save by Irish goalkeeper Shay Given but the lively front-man proved too much of handful six minutes after the break when he helped the Czechs into the lead.
Rezek's tidy pass to Baros after drawing three defenders away from his strike partner left the former Liverpool forward wide open in front of goal and he curled his finish inside Given's left hand corner.
Rezek fizzed a shot past the post just before the hour and with Ireland rarely troubling their opponent's goal, Giovanni Trapattoni's stubborn side, better known for their resolute defence than dangerous attacking, looked to be heading for a first defeat in 12 matches.
Winger James McClean, who has made a big impact for Sunderland in recent months, came of the bench to a standing ovation to make his Irish debut but it was another substitute, West Bromwich Albion's Cox, who rescued the draw.
Cox, on for team-mate Long, latched onto a Keith Andrews pass on 86 minutes and after gliding past his marker, finished well from a tight angle to keep Trapattoni's near one-year unbeaten run in tact.
"It was very important [to stay unbeaten]. I think we were a little bit flat and like on a lot of occasions, we needed to go a goal behind to wake us up a little bit," man of the match John O'Shea said.
"I think it's something we have to improve on because going into the European Championships against the calibre of teams we're playing, we can't afford to give them a goal start."
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