Northern Ireland have been plagued by poor finishing in their UEFA Nations League campaign and that profligacy came to the fore again in Thursday's friendly, with Randolph at his best.
Having made a brilliant stop to deny Gavin Whyte early on, the Middlesbrough goalkeeper pulled off two top-class saves in the second half to keep Liam Boyce and Jordan Jones at bay.
While Northern Ireland's troubles in front of goal have resulted in their relegation from Nations League Group B following Austria's draw with Bosnia-Herzegovina, Randolph's form will at least give the hosts confidence heading into Monday's potentially crucial clash against Denmark.
Randolph came to the hosts' rescue 14 minutes in, rushing out to deny Whyte after Shane Duffy's error had enabled Boyce to break clear.
Duffy should have atoned for that mistake at the other end soon after, only to mistime his header after meeting Robbie Brady's pinpoint free-kick.
Brady's set-piece deliveries continued to present the home team's greatest threat, with Darragh Lenihan sending another header at Bailey Peacock-Farrell before Glenn Whelan was taken off to a standing ovation on his 85th and potentially final cap.
Boyce looked set to break the deadlock midway through the second half, but Randolph got down to make an instinctive stop.
Randolph was not done there, though, as he lunged out to make a wonderful save with his leg to prevent Jones claiming the bragging rights for Northern Ireland.
What does it mean? Goals in short supply
Having managed just one goal from their three Nations League matches so far, Northern Ireland again failed to take their chances in Dublin.
But while Michael O'Neill can take solace in the fact that his side are creating opportunities, Brady's excellent set-pieces on his first international start in over a year seemed the Republic of Ireland's only real attacking asset.
Randolph the home side's hero
It may just have been a friendly, but given the history between these two rivals, national pride was at stake. While the performance from the Republic of Ireland will perhaps raise questions over their management team, Randolph at least provided a much-needed boost for boss Martin O'Neill.
O'Neill's tinkering makes little difference
Martin O'Neill switched to a 3-5-2 system for this encounter, but apart from allowing Northern Ireland to pressurise his defenders as they attempted to play the ball out from the back, the change achieved little. The hosts rarely mounted a sustained spell of pressure during the stalemate.
Key Opta facts:
- Republic of Ireland have lost once in their last nine international matches against Northern Ireland (W4 D4) – a 1-0 loss at home in May 1999.
- However, they have won only one of their last 10 matches in all competitions (D4 L5) and are winless in their last five (D3 L2) since a 2-1 victory against the USA back in June.
- Northern Ireland have won just two of their last 12 games in all competitions (D3 L7) scoring only seven goals and conceding 14 during this period.
- Northern Ireland have failed to score in any of their last seven away games (D2 L5), a run dating back to October 2017 – they last went longer without a goal away from home between May 1981 and October 1983 (run of nine).
The Republic of Ireland's Nations League fate could already be settled by the time they face Denmark, who play Wales on Friday. Northern Ireland, meanwhile, round out their campaign against Austria on Sunday.