Solkjaer's double strike were his first league goals at Old Trafford since he hit the target against Liverpool in a 4-0 victory three and a half years ago.
But, despite the goals, United's real man of the match was again Cristiano Ronaldo. The Portuguese star is enjoying his best ever spell for the Red Devils since joining them from Sporting Lisbon for £12.7million in the summer of 2003.
Ronaldo led a poor Newcastle defence a merry dance all afternoon, hitting the woodwork three times and coming close to scoring on numerous other occasions.
Wayne Rooney, the scourge of the Magpies since he arrived at Old Trafford, is still searching for his best form this season.
Rooney, who had scored for United in all four previous league games against Newcastle since his move from Everton in August 2004, never looked like adding to that tally.
United's other hero was surprisingly a defender with centre-back Nemanja Vidic unlucky not to score.
The 24-year-old Serb was denied his first goal for United when he connected with Ronaldo's 16th minute corner, only to see his bullet header from six yards brilliantly turned over the bar by goalkeeper Steve Harper.
In the 23rd minute, Rooney's cross from the right found Rio Ferdinand at the far post and his shot from 12 yards hit Newcastle defender Steven Taylor in the face.
United produced a superb move soon after when Solskjaer, Rooney and Ronaldo carved Newcastle open down the left, leaving an opening for Darren Fletcher on the right edge of the box with his fierce shot crashing against the post.
Ronaldo's ferocious 30-yard free-kick thudded into Harper's midriff before United took the lead in the 40th minute.
Ronaldo played a short corner with Patrice Evra before embarking on a magnificent mazy run in an arc from the left corner to the edge of the box, where he unleashed a powerful drive which hit the Newcastle post.
The ball cannoned back off the woodwork and Solskjaer, standing unmarked near the penalty spot, stuck out his leg to direct the ball into the net.
United had been building up slowly to their goal and that momentum increased after the break with a second strike in the 48th minute.
Newcastle failed to clear a Newcastle corner and Rooney lofted the ball back into the penalty area from the right.
Taylor's poor clearing header fell straight to Vidic on the edge of the box and his shot saw Solskjaer stick out his foot to deflect the ball into the net from eight yards.
United could have been 3-0 ahead within a minute. Fletcher's shot from the right edge of the box was parried by Harper at full stretch and Ronaldo, coming in at the far post, rattled the bar with his shot from six yards.
Ronaldo's hat-trick of hitting the woodwork came after 55 minutes.
Rooney and Paul Scholes again opened up Newcastle from the right and Ronaldo's low shot from six yards at the far post rattled the woodwork.
United should have had a penalty in the 66th minute when Taylor handled a Fletcher shot in the box, but the incident went unpunished.
United goalkeeper Edwin Van der Sar's only real worry came in the 73rd minute when he was forced to turn over Peter Ramage's powerful 25-yard shot.