Arsenal bid to slow Manchester United juggernaut, Manchester City juggling with injuries and more.
Coach Solskjaer could even enjoy the luxury of a 95th-minute penalty miss when Paul Pogba's effort was well saved by Angus Gunn following Stuart Armstrong's trip on Marcus Rashford.
United's lengthening injury list had given Lukaku and Alexis Sanchez the opportunity to show Solskjaer they were ready to shoulder more responsibility during the final months of the campaign.
Substitute Romelu Lukaku broke the deadlock just 38 seconds after coming on midway through the second half.
Jose Mourinho's team is now six points off the Champions League qualifying places and a massive 16 behind first-place Manchester City.
Romelu Lukaku was widely criticised after United were beaten 1-0 at home by Juventus in midweek, extending his goal drought to eight games.
Belgium's second win of the fledgling tournament keeps them flying high in League A Group 2 following an opening 3-0 win in Iceland.
Wolves visit Old Trafford on Saturday, before a trip to West Ham and a home fixture against Newcastle, by which time Lukaku could be the clear leader in the race for the Golden Boot.
Eden Hazard converted a 29th-minute penalty after a foul on Lukaku, with the Manchester United striker netting a quick-fire second before adding a third in the closing stages.
Roberto Martinez's men showed their class and no hangover from their exertions in finishing third in Russia to warm-up for their Nations League opener against Iceland on Tuesday.
Romelu Lukaku opened the scoring in the 27th minute with a simple back-post header from an Alexis Sanchez cross.
Of the 122 goals in the 48 matches so far, 31 came from players in England's top league and 29 from players in Spain.
England impressed in their opening two World Cup games beating Tunisia 2-1 in Volgograd then thrashing Panama 6-1 in Nizhny Novgorod.
England striker Harry Kane leading the race for the Golden Boot and a record World Cup win after thrashing Panama 6-1.
Lukaku's absence would be a blow to Belgium's hopes against England, with top spot in the group likely to be up for grabs.