The Exiles' other tries came from former England winger Topsy Ojo and a penalty try, with 21-year-old full-back Tom Homer kicking 26 points.
Homer produced a faultless display to land six penalties and four conversions and take his points tally for the season to 68 from four matches.
Newcastle replied with late tries from replacement prop Darren Fearn and centre Jamie Helleur, with fly-half Jimmy Gopperth kicking 19 points.
Homer kicked Irish into a fourth-minute lead with a well-struck penalty from a metre inside the Newcastle half after the visitors were caught offside.
But, four minutes later, Gopperth levelled from 45 metres before putting Newcastle ahead with his second penalty in the 11th minute.
Irish scored their opening try three minutes later when centre Steve Shingler and fly-half Daniel Bowden combined cleverly to create the chance for Ojo.
Despite slipping on his way to the line, the winger quickly recovered his footing to collect his third try in four league matches this season before the Newcastle cover could get across.
Homer landed the conversion and Newcastle suffered another blow from the restart when skipper James Hudson was yellow-carded against his former club.
Hudson looked unfortunate to be despatched to the sin bin, opposing second row man Matt Garvey landing heavily and requiring treatment after contesting a 50-50 ball as they jumped for Gopperth's kick-off.
Homer and Gopperth twice exchanged penalties before Homer landed his fourth of the match to put Irish 19-12 ahead in the 32nd minute as the Falcons repeatedly fell foul of referee David Rose.
Gopperth finally had the first miss of the match when he put his fifth penalty kick wide of the posts on the stroke of half-time.
Newcastle, who had failed to mount a single attack of note in the first half, showed much more intent at the start of the second.
A weaving run by right-wing Alex Tait put them on the attack, forcing Irish to defend for the first time.
Falcons lock Tim Swinson was denied a try when the referee brought him back for a double movement after he reached over the line to touch down - the official awarding Newcastle, who had been allowed to play the advantage, an earlier penalty.
Gopperth made no mistake, landing his fifth attempt from six kicks, to cut the deficit to four points.
But Homer responded twice, in the 48th and 58th minutes, to extend the margin to 10 points.
Irish effectively put the game beyond Newcastle's reach when England Under-20 centre Joseph picked up a dropped pass inside his own half and raced 70 metres for the home side's second try, converted by Homer.
The Falcons were reduced to 14 players for a second time when replacement full-back Will Chudley was sin-binned for offending at the breakdown in front of his own posts.
Irish elected to scrum instead of kicking the penalty and were rewarded with a penalty try, converted by Homer, as the Newcastle pack illegally disrupted their forward march.
The Falcons retaliated when Fearn forced his way over for their first try, converted by Gopperth.
Joseph took a pass from Bowden to race in for his second as a frantic finish ensued. Helleur grabbed Newcastle's second touchdown with a minute to go but the visitors had left themselves far too much to do.
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