Pogba has rediscovered his form since Solskjaer took charge at as United's interim manager in December following the sacking of Jose Mourinho.
Pogba opens the scoring by winning and converting a spot-kick for his 10th United goal of the season - equalling his best club total in a single campaign.
Despite being stripped of vice-captaincy earlier this season and dropped for the final three league games of Mourinho's tenure, Pogba said that he had no hard feelings towards the Portuguese.
The pair have been replaced by Tottenham Hotspur midfielder Moussa Sissoko and Arsenal striker Alexandre Lacazette.
Mourinho says he is sometimes frustrated with the work United does and is always expecting more.
Pogba was rested by Mourinho for the shock League Cup third-round exit against Championship side Derby on Tuesday and watched from the stands as United lost on penalties after a 2-2 draw at Old Trafford.
The midfielder reportedly has a tense relationship with United coach Jose Mourinho and has been linked to the Spanish champions.
Pogba will remain captain for the Brighton game, although Mourinho explained that Antonio Valencia will reclaim the armband when he returns to action following a calf injury.
Mathias, the 27-year-old brother of Manchester United and France star Paul, is currently out of contract having picked up an injury.
The French midfielder says if a player is not happy, they cannot give their best.
Speculation about the midfielder's future is rife, with reports of interest from Barcelona, but Ferdinand has told executive vice-chairman Ed Woodward he must keep hold of the 25-year-old.
United are without several World Cup participants, including France’s Paul Pogba, Belgium’s Romelu Lukaku and Marouane Fellaini, and England’s Jesse Lingard and Marcus Rashford among others.
Pogba was the subject of criticism from some quarters for his United performances last season and found himself relegated to the bench at times during the second half of the campaign.
Pogba had scored two goals in a remarkable second-half recovery from United as they won the Manchester derby 3-2 to deny City a win that would have seen Pep Guardiola's men clinch the title.
Victory for City would have seen Pep Guardiola's men crowned as champions and take a United record in the process by winning the title with six games to spare.
There have been numerous reports of disharmony between Pogba and United manager Mourinho, with France coach Didier Deschamps publicly suggesting the midfielder cannot be happy at Old Trafford.
Pogba says it would be a pleasure to play with Paris Saint-Germain's Neymar.
The French midfielder, who cost United £89 million, hasn't completed 90 minutes in a month, with Jose Mourinho either substituting or benching him in the last few games.
The United manager says he has to come up with a contingency plan as the French midfielder may not be available for then trip to Sevilla.
Although the Portuguese is aware of Scott McTominay's abilities having utilised him in 12 games this season.