The Belgian midfielder was one of the outstanding performers at Stamford Bridge on Saturday, helping Chelsea return to winning ways in the Premier League with a dominant second-half display.
Lavia's contribution was particularly encouraging given the injury problems which have disrupted his progress since arriving at the club. Having struggled to establish continuity during his Chelsea career, the 22-year-old is now beginning to demonstrate the qualities that made him such a highly regarded midfield prospect.
Alonso was delighted with what he saw against United and believes the midfielder's improvement has been evident over several weeks.
"It was a top performance. In the last three weeks, I've seen a Romeo in top form. He is feeling good and feeling confident," the Chelsea manager said.
"His game, from a midfielder's point of view, was very complete. He has done so many good things and I'm happy for him. He deserves huge recognition."
Lavia played a decisive role in Chelsea's opening goal, winning possession in midfield before releasing Morgan Rogers, who drove towards the United defence and lifted a composed finish over goalkeeper Senne Lammens.
It was an example of the qualities Alonso values in the Belgian, whose ability to recover possession, retain control of the ball and connect defensive and attacking phases gave Chelsea greater authority in midfield.
"He has done so many things right. He was always connecting the defence with the attacking players, he was able to switch the game, he has taken many right decisions, was very dynamic and competitive," Alonso added.
"So I think, not just this game but in the last two or three weeks, he has been playing at a very good level and I'm very happy for him."
Just as significant was Lavia's ability to complete another 90 minutes. He had played the entirety of Chelsea's Carabao Cup encounter with Liverpool at Anfield on Wednesday, making his performance against United an important test of his physical condition.
With Jordan Henderson unavailable through illness, Lavia retained his place alongside Moises Caicedo and showed no obvious signs of fatigue as Chelsea took control after the interval.
Alonso believes the midfielder's growing confidence has been central to his ability to cope with the increased workload.
"We knew Jordan was not feeling that well and we know Rom is feeling better, is feeling stronger, is feeling more confident to go with more minutes and with more load," he explained.
"And he's gone from playing the whole game at Anfield, to not even 72 hours later playing that way and with that energy [against Man United]. Sometimes the head is more important than the legs and now his head is in a good place."
For Chelsea, Lavia's progress offers encouragement beyond the result against United. His availability and ability to influence matches could become increasingly important as the fixture schedule intensifies, while Alonso will hope the midfielder can finally put his injury interruptions behind him.