1. Man United cruise to victory

The optimism is back at Manchester United. This routine win over Stoke City helped, but so has the mounting speculation that the Old Trafford club are set to win the race for Alexis Sanchez.

City's lead at the top of the Premier League table is down to 12 points after their 4-3 defeat to Liverpool at Anfield on Sunday and the glimmer of hope United fans still have has been made that little bit brighter by the prospect of Sanchez wearing United red rather than City blue for the rest of the season.

Sources have told ESPN FC that club chiefs are growing increasingly confident the Chilean forward will sign this month and that Jose Mourinho said before this game that Henrikh Mkhitaryan had been left out because of "doubts" about his future -- after saying on Friday he would be involved -- will only fuel talk that he is heading to Arsenal as a makeweight.

On the pitch -- despite driving rain at Old Trafford -- the feel-good factor was inspired at first by Antonio Valencia. Back after missing six games with a hamstring injury, United's captain cut inside Joshua Tymon after nine minutes and curled a fantastic effort into the far corner. Valencia looked as surprised as anyone that it came with his left foot.

Stoke had three half chances that had new manager Paul Lambert, appointed before the game, off his seat in the directors' box, but there was not much his team could do to stop United scoring a second after 38 minutes.

Paul Pogba, who was excellent all night, picked out Anthony Martial in his peripheral vision on the edge of the box and the forward curled in his 10th goal of the season. It was a moment that showed why it is Mkhitaryan, rather than Martial, is likelier to be on his way to the Emirates Stadium.

Romelu Lukaku scored his 17th goal of the season after 73 minutes to add the finishing touch to a comfortable night on which United barley got out of second gear.

2. Pogba runs the show

When Pogba signed for United in a world-record £89.3 million move from Juventus in 2016, Mourinho said the French midfielder would, eventually, look like a bargain. However, perhaps even United's manager didn't realise it would only take 18 months.

An unrecognisable transfer market -- one in which Neymar costs £198 million -- is part of it, but so is Pogba's form. His range of passing against Stoke was sublime; one 60-yard effort to Luke Shaw seemed to check back on itself and allow the left-back time to catch up and cross.

By half-time, Pogba had two assists. The first came after he battled through midfield to poke the ball to Valencia and the second was the result of wonderful vision to square the ball to Martial. Indeed, the pass was only bettered by Martial's finish.

Mourinho is fond of saying there are two Uniteds: One with Pogba and one without. The 24-year-old has missed 15 games in all competitions this season through a combination of injury and suspension. It will be a source of frustration to his manager that he has only been able to pick Pogba against a top-six side once: The impressive 3-1 win at Arsenal in December.

United might be closer to City if their main man had been available more often; Pogba now has nine league assists this season -- level with Kevin De Bruyne and Leroy Sane -- despite only playing 13 games.

3. Lambert sees the size of Stoke's task

Lambert chose not to take charge of the team at Old Trafford after being appointed as Mark Hughes' successor on Monday but, watching from the directors' box, he will have have seen some things he liked. Stoke had a good spell midway through the first-half and Stephen Ireland, making his first league start since 2015, missed two good chances.

But Lambert will also know that his new club is on a run of one win in nine games in all competitions and lay 18th in the Premier League. They will not have expected much from a trip to Old Trafford -- Stoke last won here in April 1976 -- but seeing their name in the relegation places will not make pleasant viewing.

Their next four games -- three of them at home -- could be make or break; Huddersfield, Watford, Bournemouth and Brighton offer a chance to move away from the bottom three.

It is a run that also offers the new manager a chance to get Stoke's fans on his side. There was a brief chant of "Paul Lambert's red-and-white army" from the travelling supporters inside Old Trafford but the majority appears underwhelmed that the Scot, who has been out of work since leaving Wolves in the summer, has been handed a two-and-a-half year deal.

It is not the name supporters were expecting, but they won't care if their club is still in the Premier League come August.