Pearson produced a trademark run and offload to set up Langdon, who finished well to finally give the black, green and gold the lead in torrential rain at Kingston Park.
Newcastle threatened to level things late on as Saints full-back George Hendy was yellow carded and Iwan Stephens went in out wide for the Falcons.
But fly-half Brett Connon couldn't slot a tricky conversion to level the scores, and Saints managed to hold on to secure their first Gallagher Premiership win of the season.
Phil Dowson's men had headed north on the back of league losses to Sale Sharks and Bristol Bears, and they were without 14 players due to injuries and international duty.
They also had conditions to contend with at Kingston Park as the rain was pouring down when the teams entered the field.
And Saints found themselves submerged early on, conceding a couple of penalties, the second of which Connon slotted to give the Falcons the lead.
Saints used box kicks to try to gain some territory, and they soon won a scrum penalty following a knock-on, allowing Fin Smith to level the scores from the tee.
But Falcons responded with a scrum penalty of their own as Ethan Waller was penalised, allowing Connon to put the hosts back in front.
It was a game full of huff and puff, with the slippery conditions preventing any real rugby being played.
Both sides were living off mistakes from the opposition, and Saints were able to level the scores again after Falcons infringed in defence, allowing Smith to slot his second penalty.
The half ended with a scrap for possession, which summed things up nicely at the end of a first 40 minutes that were a tough watch, and probably even tougher to play a part in.
Falcons had the first chance to add to their tally in the second period, winning another scrum penalty to set up a shot at goal for Connon, but the fly-half sent his effort wide.
The game was badly in need of a spark, and Pearson proved to be the catalyst.
The Saints flanker made a blistering break and delivered a perfect offload out the back for the onrushing Langdon, who showed great strength to get to the line and get the ball down.
Smith converted and Saints led for the first time at 13-6 with 25 minutes still to play.
Falcons soon had the chance to issue a response as Saints gave away a cheap penalty for obstruction on halfway and the home side went to the corner.
The lineout surge was defended well but when the ball came out, Fraser Dingwall was penalised, meaning Connon was able to cut the gap to four points with the kick.
Smith soon restored the seven-point advantage as Falcons gave up another penalty inside their own half.
Saints looked to be taking a little control, but after losing a lineout on halfway, they suddenly invited huge pressure.
Falcons applied the squeeze, winning penalty after penalty, leading to Hendy earning a yellow card.
And eventually the score came as wing Stephens went over out wide.
It left a tough conversion to level the scores, and Connon couldn't make it, seeing his effort shave the right post and go wide.
Saints were two points up with three minutes to go and as the clock ticked down, Tom James decided to kick the ball away into the Falcons 22.
It allowed the home side to clear, forcing George Furbank to kick into touch.
The Falcons set up one final attack, but after they went wide, James did superbly to get over the ball and win a penalty, which made sure of a gritty away success for Saints.
Newcastle Falcons: Obatoyinbo (Orlando 53); Radwan, Penny, Jennings, Stephens; Connon, Stuart (O'Sullivan 67); Brocklebank (Brantingham 57), Blamire (Byrne 57), Tampin (McCallum 53); van der Walt (Hawkins 64), de Chaves (Lockwood 64); Cross (Lockwood 62), Pepper, Chick (c).
Saints: Furbank (c); Seabrook, Dingwall, Hutchinson, Hendy; F Smith, James; E Waller (A Waller 48), Langdon (Cruse 69), Davison (Millar Mills 64); Munga (Moon 64), Coles; Scott-Young, Pearson, Graham.
Referee: Hamish Smales