Giorgi Gabedava's injury-time penalty ended Connah's Quay Nomads' Europa League qualifying hopes at the Racecourse.
Callum Roberts was penalised for a challenge as Dinamo Tbilisi sought a winner.
Gabadeva stepped up to tuck his shot into the left-hand corner of the goal.
That sealed victory against a threadbare squad after the game went ahead despite three Nomads players testing positive for Covid-19.
The trio and two additional players showing symptoms were put into self-isolation.
Manager Andy Morrison later said the club "had to turn a blind eye" to three players who turned up to play on Thursday feeling unwell.
Nomads had dropped into the Europa League after FK Sarajevo beat them 2-0 in the Champions League first qualifying round at Cardiff City Stadium in August.
Wrexham's Racecourse ground hosted the one-off tie as Connah's Quay's home ground is not deemed Covid-compliant.
And while Nomads were happy not to travel to the Welsh capital, there was no hiding their disappointment after matching Dinamo, Georgian champions for the last two seasons, for 90 minutes.
Connah's Quay Nomads
- 1BrassBooked at 36mins
- 22DaviesBooked at 69mins
- 4FarquharsonBooked at 53mins
- 16OwenBooked at 38mins
- 10InsallBooked at 45minsSubstituted forWilliamsat 87'minutes
- 19Gbegnon Amoussou
- 16KimadzeBooked at 64mins
- 18OrsulaSubstituted forRodrigues da Silva dos Santosat 59'minutes
- 7ZariaBooked at 46minsSubstituted forKapanadzeat 80'minutes
- 38KavtaradzeSubstituted forKloosterat 90+5'minutes
- 3Mongil Adeva
- 17Rodrigues da Silva dos Santos
- Alain Durieux