An excellent lofted finish from Dawson just a minute before half time got the Foxes' noses in front before Cain finished a nice counter attacking move to seal the points with seven minutes left.
Captained by James Pearson at right-back, Steve Beaglehole’s side moved into the top half of the league table with the victory and avenged their narrow U21 Premier League Cup exit in December.
Manager Steve Beaglehole told LCFC.com: “Overall I’m really pleased with how they’ve done. It was a great team performance and the lads showed a great work ethic throughout.
“We dominated the game and created plenty of chances, but we said to the players beforehand that the goal was to win with a clean sheet, which they have done, so credit to them."
The Foxes made a steady start to the fixture at Whitley Park - the centre back pairing of George Taft and Kieran Kennedy doing a fine job of keeping Newcastle’s Michael Richardson at bay in the opening exchanges.
Big striker Jacob Blyth led the line for City, supported by the lively Harry Panayiotou, and both were denied by Magpies ‘keeper Jak Alnwick early on, before Cain’s follow-up went wide of the mark.
Newcastle’s Jonathyn Quinn then drew a save from Adam Smith
, but City’s excellent work-rate soon saw the game veer in their favour.
Taft tested Alnwick from a corner before Blyth blazed wide after some neat footwork inside the Newcastle box, meaning it was down to Dawson to eventually make the breakthrough just a minute before half time.
The tricky winger, who also netted against the Magpies in December, managed to beat the impressive Alnwick with a nice chip after he saved Blyth's initial shot once the Foxes had relieved the home side of possession in their own half.
Neither side were able to truly impose themselves on proceedings in the second 45 minutes, although the Foxes weren’t made to work too hard in order to hang onto their lead.
Newcastle’s best hopes of beating Smith came and went when Rolando Aarons’ appeals were a penalty went unheeded by the referee, leaving City to wrap up the points seven minutes from time.
The goal came from a Magpies corner, which was well dealt with by the Foxes before a sweeping breakaway move ended with Panayiotou setting up Cain to slide the ball past Alnwick for an excellent 2-0 victory.
Next up for Beaglehole’s Foxes is a tough trip to league leaders Fulham on Monday 17 February.
NEWCASTLE: Alnwick, Sterry, Satka, Williams, Gibson, Richardson, Logan, Kemen, Aarons, Olley, Quinn
SUBS: Mitchell, Booth, Drennan, Roberts, Gilliead
CITY: Smith, Pearson (c), Elder, McCourt, Kennedy, Taft, Dawson, Cain, Blyth, Panayiotou, Dodoo
SUBS: Frempah, Simpson, Anton, Paratore, Barrington
GOALS: Dawson 44, Cain 83