The Republic, who went into the game having won just once in their previous nine outings and desperate to gain some momentum ahead of Monday night's Nations League trip to Denmark, were second-best in a clash between neighbours which demonstrated their respective difficulties.
But they needed Randolph to make fine saves from Gavin Whyte and substitute Jordan Jones either side of the break to ensure they emerged with something to show for their efforts as the visitors, who had tasted victory only twice in 11 matches before kick-off, created the better openings.
Indeed, the home side's only chances of note predictably came courtesy of Robbie Brady set-pieces on the Burnley midfielder's return to the international stage following a year out through injury, and the final whistle was greeted by a chorus of boos.
The reception afforded to the two national anthems was less than respectful, but in a cagey start to the game it was the visitors who almost broke the deadlock after Shane Duffy had misjudged Steven Davis' 14th-minute ball forward.
Duffy's error allowed Liam Boyce to hook the ball into the path of Stuart Dallas to in turn feed Whyte, who looked certain to mark his first senior start for his country with a goal until Randolph raced from his line to make a vital block.
Seamus Coleman and Boyce were left bloodied by a clash of heads seconds later as Northern Ireland continued to press, but Duffy should have atoned for his earlier error when he met Brady's 21st-minute free-kick, but got his timing wrong to allow keeper Bailey Peacock-Farrell to tip his downward header over.
Dallas might have done better after cutting out Glenn Whelan's crossfield ball and curling a shot harmlessly wide, but with he, Davis and Whyte dominating in midfield, the visitors looked the more likely scorers.
Whelan's 85th and probably final Ireland appearance came to a planned end nine minutes before the break as he was replaced to warm applause by Conor Hourihane seconds before James McClean, booed at every touch by the travelling fans, lashed an ambitious volley high over.
However, Randolph was called upon once again four minutes before the break when, after Darragh Lenihan's ball had been intercepted, Davis picked out Dallas' run and saw him force a solid save from the Middlesbrough keeper, who was relieved to see Michael Smith's stoppage time piledriver fly just over his crossbar.
The Republic returned determined to wrest control from the visitors and enjoyed a measure of success as they managed to ease themselves further up the pitch, and they went close when Callum Robinson steered McClean's 59th-minute shot wide after Coleman had crossed from the right.
Boyce looped a header over from Smith's 65th-minute cross as Northern Ireland responded and then saw the ball hacked away as it broke into his path after Randolph had parried Smith's volleyed delivery three minutes later.
The keeper came to the Republic's rescue once again with 18 minutes remaining when, after substitute Jones had pounced on another mistake by Lenihan, he denied the midfielder with his foot.