Atletico were left to rue a number of missed chances by Diego Costa as they failed find an equaliser after Prochazka had bundled in Michal Duris' flick-on from a corner after 26 minutes.
And Costa's evening went from bad to worse in stoppage time as he was shown a straight red card for needlessly getting involved in a melee after his side had a goal ruled out for a foul by the Brazilian on goalkeeper Matus Kozacik.
With both sides already through to the last 32, first place was all there was left to play for and the holders' failure to secure top spot could be significant as they could now meet the likes of Champions League winners Chelsea in the next round.
Atletico boss Diego Simeone picked a slightly stronger side than he had in previous games in the group stage with five of those involved in the Madrid derby on Saturday starting and two of them nearly combined for the opener on 16 minutes as Juanfran freed Adrian, but the striker's shot just flew past Kozacik's left-hand post.
However, the visitors were soon behind as Prochazka was in the right place at the right time to fire home from close range after Duris had flicked on a corner at the near post.
Costa then had two good chances to equalise as he fired just wide from the edge of the area on 32 minutes before wasting a golden opportunity by shooting straight at Kozacik when clean through six minutes later.
Koke also saw an effort fly just off target after the break as the Spaniards searched for the equaliser, but after Costa was again denied by some smart reactions by Kozacik 25 minutes from time they never really created another clear-cut opening.
The Plzen keeper was perhaps slightly fortunate to get a foul when he spilled a looping cross under pressure from Costa in stoppage time and substitute Pedro Martin poked home the loose ball, but Costa was unwise to get involved in what followed and his red card will mean he is suspended when the competition gets going again in February.