United arrived in London smarting from their 5-0 home defeat by their fiercest rivals last week, which led to a storm of speculation over the future of the Norwegian boss.
But a sublime first-half strike by Ronaldo, a clever finish from Edinson Cavani and a late Marcus Rashford goal lifted the visitors to fifth in the table, just three points behind third-placed Manchester City.
Solskjaer paired veteran forwards Ronaldo and Cavani up front for the first time, with Mason Greenwood and Rashford missing out.
He also opted for a central back three, bringing in the returning Raphael Varane alongside Harry Maguire and Victor Lindelof.
The game took time to catch fire in front of a crowd of more than 60,000, with clear-cut openings at a premium.
