The Norwegian international netted just before and after half-time on Sunday, his first goals at Old Trafford for over three years, as United easily breezed past a lackluster Newcastle United side.
Cristiano Ronaldo was once again on scintillating form and Solksjaer was on hand to profit after the Portuguese winger's 41st minute strike thumped back off the post.
United and Solksjaer's second came when he deflected a Nemanja Vidic shot past Newcastle keeper Steve Harper.
Darren Fletcher had earlier rattled the woodwork and Ronaldo did so again later in the second half as Newcastle simply fell apart.
They needed some good saves by Harper to keep the score respectable and never looked remotely capable of ending their 34-year run without a league win at Old Trafford.
Cry for me Argentina
Elsewhere in the Premiership on Sunday West Ham continued their miserable start to the season losing at home to Reading.
The unexpected arrival of Argentinian stars Carlos Tevez and Javier Mascherano in August had raised expectations of Hammers fans to new levels but Alan Pardew's side have found absolutely no rhythm since.
Instead it was supporters of Pardew's old side Reading who had something to shout about after South Korean winger Seol Ki-Hyeon struck after just 80 seconds with a superb long-range effort.
Reading fans have still to forgive Pardew for his acrimonious departure from the club three years ago.
Carlos Tevez tested Reading goalkeeper Marcus Hahnemann with a couple of long-range efforts but the closest West Ham came to equalising was a Yossi Benayoun strike that was cleared off the line by Steve Sidwell in the final moments.
There was good news for another London club on Sunday trying to recover from a poor start to the season.
Spurs celebrate only their second
win of the season
A backheel from Danny Murphy and a penalty from Jermain Defoe finally gave Tottenham Hotspur liftoff and condemned Portsmouth to their second defeat in a row having gone five games without conceding.
Murphy back-heeled Tottenham into a first minute lead after David James had failed to hold Dimitar Berbatov's header.
Defoe increased the advantage when he scored his first goal of the season from the spot after Pedro Mendes was penalised for a foul on Didier Zokora.
Television replays suggested referee Chris Foy had got it wrong as Zokora went to ground even though the former Tottenham midfielder Mendes had made no contact.
Nigerian striker Kanu pulled one back just before half time as he scored his fifth goal of the season with a powerful header from Gary O'Neil's cross.
Rovers roll on
Blackburn Rovers striker Benni McCarthy grabbed a late winner as his side beat Wigan 2-1 at Ewood Park for their fourth win in a row.
Blackburn goalkeeper Jason Brown, making his debut as a second half substitute, grabbed his share of the plaudits after saving a penalty minutes before his team's winner.
Emile Heskey had given Wigan a second minute lead with an impressive finish from Emmerson Boyce's cross.
South Africa star McCarthy spurned a series of chances before David Bentley curled in an excellent equaliser on the stroke of half-time, his second long-range beauty in a week.
Paul Jewell's side had a chance to go in front when Andre Ooijer's 77th minute challenge on Heskey was adjudged to be a penalty.
But Svetoslav Todorov's spot-kick was saved by Brown and Blackburn clinched a fourth successive win when McCarthy scored nine minutes from full time after Jason Roberts set him up.