Bournemouth boss Howe hailed midfielder Arter for keeping his raw emotions in check after he and his partner lost a child at birth in midweek.
Arter was close to tears when booked for a fulsome challenge, with Cherries boss Howe embracing his combative star on the final whistle.
Manager Howe hailed an unprecedented week for Bournemouth, after the 1-0 win at Chelsea, backing the promoted club to win their fight for Premier League safety.
"It's been a really tough week for Harry and his family, naturally," said Howe.
"Life has a way of throwing these things at people and families, and it's been a hugely emotional week for him.
"I think he's handled himself with real dignity throughout the process, and to play the way he did today, with the emotions running through his body, I can't credit him enough for that.
"He showed real strength to keep his emotions in check, and I've got to say his team-mates rallied around him really well.
"There were some emotional scenes in the dressing room afterwards.
"I'm really proud of him, but the pain for them won't go away, so we'll have to look after Harry, and our thoughts are with him and his family at this time.
"Harry wanted to play, there was no doubt in his mind that he wanted to play.
"I had to make an assessment of him and how he looked to me and have a chat with him.
"But there was no doubt once I'd spoken to him that I was going to play him today."
Junior Stanislas opened the scoring by curling home direct from a corner at Dean Court.
United equalised through Marouane Fellaini's scruffy finish, but Bournemouth struck back and sealed the win through Josh King.
Bournemouth toppled United 2-0 in 1984's FA Cup under Harry Redknapp, with current boss Howe admitting he perhaps undervalued that achievement in cherishing his side's victory over Chelsea last week.
Keen not to repeat that feat, Howe admitted Bournemouth still managed to break new ground by backing up victory at Chelsea with the United triumph.
"I think I probably prefer to focus on the week rather than the individual games," said Howe.
"Last week I felt afterwards I felt maybe I disrespected Harry a bit given his win over Manchester United, that was a terrific achievement for that group of players and him.
"But if you look back on this week it's been a great week for the club and not the type of thing that's ever happened here, so we're certainly embracing the good feeling at the moment."
Meanwhile, Louis van Gaal challenged Manchester United to win their next three matches to sustain their Premier League title hopes.
Frustrated boss Van Gaal blasted the sloppy defending that led to Bournemouth's victory, insisting United must heed a 'strong lesson' from defeat.
''I think that we have the selection to do that (win the league), but we are now in a very difficult position,'' said Van Gaal.
''We have to make a revival this week, and that's always very difficult because you have lost two in a row, and that doesn't happen often for Manchester United.
''Two set plays, two goals: you cannot accept that as a manager, a player, a team, because we pay a lot of attention to it.
''Bournemouth benefit a lot in the corners and free-kicks and we have seen that, but still they scored twice.
''Also against Wolfsburg it was already the reason why we lost, so it's a very strong lesson for us.
''Of course I'm concerned because we have lost two matches in a row, and that is not a usual thing, so we have to stick together and prepare for our match against Norwich."
Now the beleaguered Dutch boss has called on his men to see off Norwich City, Stoke City and Chelsea before the turn of the year to keep their title hopes alive.
''Of course it's disappointing if you lose two matches in a row in an important week, so now we have to stay there in a position to keep fighting," he said.
''But still we are in a position, but we have to win. 'We have now to win three matches in a row for example, to be there still after Christmas.''