The victory sees Dean Richards' side leapfrog their opponents and climb up to eighth in the Aviva Premiership table but they certainly had to earn it the hard way at Kingston Park.
Ofisa Treviranus went over for the Exiles in the first half but Humphreys and Rory Clegg were both wayward from the kicking tee all game long to keep it a low-scoring affair.
All week the Falcons have spoken about making their home a fortress this season after defeats against Gloucester and Bath.
Irish meanwhile came into the clash with three wins in a row in all competitions stretching back to their surprise success over Harlequins in the Aviva Premiership.
But wet, slick conditions made free-flowing rugby difficult for both sides and it was Richards' troops that had the chance to open the scoring but Clegg's penalty drifted wide.
And the Falcons were made to pay for that profligacy as Irish notched the first try of the game, just reward for their invention in the opening stages.
Sailosi Tagicakibau came off his wing looking for work and quick hands involving Topsy Ojo down the short side put flanker Treviranus over in the tenth minute, Humphreys off target with the conversion.
That score appeared to wake the Falcons from their slumber however and they finally began to exert some influence with ball in hand.
And they got on the board in the 18th minute as Clegg made up for his earlier miss by slotting two penalties to make it 6-5.
But on the stroke of half-time Irish were back in front as Humphreys slotted his first penalty of the game for an 8-6 lead.
After the interval the Irish pack appeared to have had a re-think and they began to get a nudge on at scrum-time, winning a penalty in a kickable position in the 44th minute that Humphreys dragged wide.
Clegg followed suit for the Falcons, pulling his long range penalty wide in the 49th minute as both sides struggled for rhythm.
The game was becoming something of a kicking contest as both sides traded bombs in the swirling wind but the Exiles remained the more adventurous.
Humphreys finally slotted a penalty for an 11-6 lead and the Falcons were right up against it.
But gradually they began to turn the screw after the hour mark and it finally told when Powell skipped clear to touch down, Phil Godman on as a replacement for Clegg added the conversion and the Falcons were 13-11 up.
Humphreys missed almost immediately with a long-range penalty before being replaced by Shane Geraghty.
And the England international had the chance to win it with the last kick of the game but his effort fell agonisingly short and the Falcons held on to take what could prove to be a crucial win.