Newcastle took the lead after 21 minutes with a superb goal from 20-year-old Jenas who lashed in a first-time shot from 20 metres after United failed to clear a Newcastle free-kick.
Solskjaer equalised after 32 minutes when he beat the off-side trap and showed great individual skill by chesting down a clipped pass from Giggs and shooting on the turn past Shay Given.
Scholes first goal came after a crisp passing move by United which he ended by volleying a one-two with Solskjaer through Given's legs. His second was set up by a typically jinking run by Giggs. A touch-on from Wes Brown set up Scholes who lashed the ball wide and high of the Newcastle keeper from the edge of the box.
United went 4-1 up in the 44th minute when Giggs scored.
John O'Shea, doing a fine impersonation of Giggs himself by dancing past Nolberto Solano and Aaron Hughes set up the goal, crashing his rising shot against the bar. The rebound fell to Giggs who slammed the ball past Given.
Scholes completed his hat-trick after 52 minutes when he planted a cross from substitute Gary Neville wide of Given and a despairing defender on the line.
The sixth came five minutes later when Van Nistelrooy sent Given the wrong way from the penalty spot for his 36th goal of the season after Titus Bramble had tripped substitute Diego Forlan in the box.
Newcastle pulled one back two minutes from time after a poor Barthez clearance allowed Shola Ameobi to grab a consolation.
The match continued the high-scoring sequence between the teams and gave Sir Alex Ferguson the double over Sir Bobby Robson this season after their 5-3 victory over Newcastle at Old Trafford in November.