There was a let off for Newcastle on 30 minutes when Bramble misjudged a long ball over the top from Brocken, but Dos Santos fired over the bar when it looked as though it had opened up for him.
Hughes was booked on 35 minutes for a foul on Brocken, but despuite the angry reaction of the Norwegians it looked as though the United man had won the ball.
Valerenga were looking the stronger team as the half drew to a close, and Given did well to tip a Brocken free kick over his bar after a couple of attacks from the visitors had csaused problems at the back..
In first half stoppage time Bramble flashed a header just wide from Robert's free kick after Hagen's foul on Shearer, but the crowd were not happy at the break and booed the team off.
Sir Bobby made a change at the start of the second period, with Shola Ameobi replacing Bellamy in attack after the Welshman was forced off with a hamstring problem.
And Ameobi had an immediate impact, cutting inside from the left to send in a low shot which the goalkeeper made a complete mess of to give United the lead again just a minute into the second half.
Robert then won a free on the left moments later in a dangerous position, but Valerenga cleared their lines then Bridges then had a shot parried after a good run from midfield, and Jenas was just unable to stretch high enough to nod in the rebound.
Robert took a great touch to get a long ball under control on the left channel, but his low cross was diverted for a corner, and the away team eventually cleared their lines after Jenas then Hughes tried their luck from the edge of the box after the corner wasn't properly dealt with.
Valerenga won their first corner of the half on 62 minutes when Hughes diverted Brocken's cross, and even though the corner was dealt with it took United time to get back possession as the Norwegians pressed for a leveller.
Bramble was just off target with a looping header after towering above his marker to get on the end of a cross from Bridges on 66 minutes, then at the other end Woodgate cut out a pass from Berre that lo0oked like it was going to send Dos Santos clear on goal.
Shearer hooke a volley just wide from O'Brien's cross as Newcastle kept up the pressure as they searched for a third goal on the night, then Valerenga made a change on 69 minutes when their player-manager Rekdal was replaced by the scorer in the first leg, Runar Normann.
Waehler fired a low shot into a crowded box on 73 minutes that was deflected away, then Brocken tried his luck from distance that flew just over the crossbar.
Brocken was then cautioned for dissent after Jalland had fouled Shearer, then on 76 minutes Brittain got his first taste of senior action when he replaced Bridges on the right side of midfield.
United won corner on 84 minutes when Shearer's shot on the turn was deflected, but Hagen rose above Bramble to head clear, then at the other end Berre should have done better than volley over from well inside the box after a cross from the right fell nicely for him.
The Magpies wrapped the game up on 89 minutes when Shearer sent Jenas racing free down the inside right with a great ball, and the midfielder elected to square the ball to Ameobi when he could easily have shot, and the striker gobbled up the chance to make it 3-1 and 4-2 on aggregate to book United's place in the last 16.