Goals in each half from Nemanja Matic and Paul Pogba sealed a happy return to Old Trafford for Solskjaer, who received a rapturous reception before kick-off.
The victory, which followed a 5-1 thrashing of Cardiff City in their first match since Jose Mourinho's departure, means the Red Devils are back to within five points of the top four having played a game more than Arsenal and Chelsea.
Huddersfield, who got a goal back late on through Mathias Jorgensen, are bottom of the Premier League table and five points from safety.
United should have been behind in the first 10 minutes, Terence Kongolo slicing a shot over the crossbar from barely five yards out after a long throw was flicked on by Alex Pritchard.
The visitors kept United at bay until 28 minutes in, when Matic tapped in after Victor Lindelof's header was blocked on the line.
Diego Dalot shot wide from a Marcus Rashford cross and Huddersfield threatened to punish that miss with a good start to the second half, in which Laurent Depoitre was denied acrobatically by David de Gea.
That save proved pivotal as, three minutes later, United doubled their lead. Juan Mata danced his way into the penalty area and found Ander Herrera, who teed up Pogba to sweep home first time.
Pogba added gloss to the scoreline and a super personal display with 12 minutes to go, collecting Jesse Lingard's pass and bending a sublime low strike past Jonas Lossl from 25 yards out, making Jorgensen's late tap-in mere consolation.
United building momentum under Solskjaer
This was not as slick a performance as United produced at Cardiff, but they largely kept Huddersfield under control and certainly played the majority of the match on the front foot.
Back-to-back wins under Solskjaer will only help to boost morale after those tough final few months under Mourinho, and Arsenal and Chelsea will play later on Wednesday knowing that anything but a win will give United hope in their quest to catch the top four.
As for Huddersfield, who have lost 13 of their 19 league games this season, their chances of survival are looking increasingly slim.
Pogba full of smiles again
In a week in which he released his only emoji app, Pogba put in a performance of undeniable joy. His goals were expertly taken, but his all-round impact was best summed up when he won back possession near his own penalty area and fired a pinpoint 70-yard pass to Marcus Rashford.
