Bedlington raced into a two-goal lead, only for Easington to respond through Jack Pounder and Luke Page.
However, Norris raced through in the second minute of injury time to slot home and give the Terriers a much-needed three points.
Easington manager Paul Frame made six changes from last week’s defeat at Billingham Town with Chris Freeman, Reece Kenney, Jake Fenton, David Paul, Liam Adamson and Callum hope all coming in for Chris Pearson, Ian Redman, Aaron Croft, Bryan Norton, Peter Jones and the now-departed Joe Kerridge.
Josh Lincoln was once again named on the bench, as was new signing Michael Bulmer.
A fast-paced start saw the Colliers try to play the ball on the floor but Bedlington broke the deadlock with their first chance in the sixth minute. A deep corner was too heavy but it was swung back into the penalty area where Josh Rodgers rose highest to plant a header into the net.
And, in the worst possible start for Easington, Rodgers collected his and Bedlington’s second in only the 10th minute. Kyle Donaldson was unable to collect a deep free-kick and it dropped to Rodgers who was able to stab home to silence the majority of the crowd.
Just before the quarter of an hour mark, the hosts almost pulled a goal back as good work from Page worked the ball out to Pounder and his powerful effort clipped the crossbar on its way over.
Following their terrible start, Easington tried to settle down and created a few chances as both Paul and Adamson went close to no avail.
Seven minutes before the break, Pounder’s great cross found Adamson free at the back post but he couldn’t find the desired connection and the ball bounced narrowly wide in what was a real let off for the visitors.
Easington went into the break in a similar position to last week’s game at Billingham Town and a vast improvement would be needed in the second half.
With the wind now on their side, the Green Army came out for the second half looking to half the deficit.
Hope went close when his free-kick was curled not too far over in the 52nd minute while Paul’s effort three minutes later was blocked by Paul Wardle.
The game then quietened down with substitutions affecting the flow of play. Aidan Goodey was busy lifting balls into the Bedlington penalty area but they were all dealt with.
Twenty minutes from time, Easington substitute Norton tried his luck from 20 yards but his effort was deflected behind for a corner while the same man was almost played in a minute later but Kenney’s through ball was slightly too heavy.
Easington’s persistence was to pay off though as Pounder made it game on in the 73rd minute. The former Sunderland RCA man collected the ball on the edge of the penalty area before firing an effort which managed to bobble into the far corner.
Now only one goal behind, Easington’s heads were up and pressure was being piled on Bedlington Terriers.
Hope’s 80th-minute cross almost found Paul at the back post but he just couldn’t bundle home while Hope’s low driven effort was well held by David Stewart.
With less than two minutes of normal time to go, Easington eventually managed to pull level. Page collected the ball on the edge of the penalty area and scuffed an effort which was destined for the bottom corner. A Bedlington defender looked to clear off the line but could only divert the ball into his own net and the Green Army were level.
However, heartbreak was to follow as Bedlington snatched a winner totally against the run of play.
A routine ball through saw Sam Norris outmuscle two defenders before running down on goal and slotting under Donaldson to seal the points for the Terriers.
It was another disappointing afternoon for Easington who go again away at Durham City next week.
Full-time: Easington Colliery 2-3 Bedlington Terriers
Easington Colliery: Donaldson, Freeman (Doyle, 59′), Goodey, Ball, Kenney (c), Pounder, Fenton, Page, Paul, Adamson (Norton, 69′), Hope
Unused subs: Anderson, Bulmer, Lincoln
Bedlington Terriers: Stewart, Locke, Henderson, Rodgers, Armstrong, Wardle, Graham (Lowery, 81′), McMahon, Hall, Scott (Norris, 67′), Oliver (c)
Unused subs: Wells, Clark, Scarth