There were rare strikes from Harry Maguire and Jesse Lingard too, completing a morale-boosting victory after back-to-back Premier League defeats.
Maguire opened the floodgates with a long-range strike into the top corner and goals from Dalot and Lingard soon followed to put the visitors 3-0 up inside 16 minutes.
Phil Jones headed United's fourth and Anthony Martial's deflected shot made it 5-0 before Mason Greenwood scored a penalty in the second half to wrap up a win that affords under-pressure Solskjaer some breathing space.
After 10 cagey opening minutes, United found space to exploit around the Tranmere box and Maguire strolled forward with the ball before cutting onto his right foot and sending a crisp drive into the top right corner from 20 yards, a slight deflection helping it on its way.
Three minutes later Dalot played a one-two with Martial and skilfully cut inside his marker before hammering an angled drive low into the far corner of the net to double his side's advantage.
Maguire continued his attacking forays and created space on the edge of the box for Lingard to curl United's third into the bottom corner with aplomb, and five minutes before half-time Jones met an Andreas Pereira corner with a looping far-post header over goalkeeper Scott Davies.
Martial rendered the second half a formality when he scored from the left corner of the Tranmere box with a shot that took a wicked deflection and curled just inside the right post.
Substitute Tahith Chong was scythed down by Davies early in the second half and Greenwood rolled his penalty into the bottom left corner.
Dalot broke down the right and lashed a shot towards goal that Davies could only parry away at the near post before Morgan Ferrier missed a one-on-one with Romero at the other end.
Lingard might have scored what would have been just his third goal in 42 games when he tried a bending shot from the edge of the box, but it flashed narrowly wide as a seventh strike eluded United.