The Norwich City winger was in electric form at the Liberty Stadium to send the Three Lions further clear at the top of their group table, with just two games left to play.
And head coach Southgate was left pleased with his side’s performance, in a match which he had billed as being England’s hardest yet in the build-up.
Wales U21s 1-3 England U21s
UEFA European U21 Championship
Qualifying Group One
7.30pm, Monday 19 May 2014
Liberty Stadium, Swansea City FC
Live on Sky Sports
"I’m really pleased with the way that we passed the ball and the creativity that we’ve shown," he said.
"From the very start of the game we played with freedom and I think we’ve expressed ourselves and created any number of chances.
"I felt towards the end, we might have seen the game out a bit better and we just need to learn a couple of things in terms of dealing with the counter attack.
"But I’m being harsh there because what this group of players has given all season has been outstanding."
Redmond has proved to be a real thorn in the side of Wales this season, after previously scoring the winner against them in the reverse fixture at Derby in March.
And Southgate wasn’t surprised to see the former Birmingham City ace in top form again to fire England one more step towards next summer's Euro Finals in Czech Republic.
"He’s a young player who has so much talent and we’ve been able to give him a bit more freedom and get him thinking about playing in more advanced areas," he told TheFA.com.
"He’s so willing to work for the team, that at times he can do too much without the ball and that can take the emphasis away from what he can do with it.
"He’s such a handful, not only with the goals that he scored but also the chances that he created and the runs that he had.
"I’m delighted for him, because he’s another player who has been a delight to work with."
Southgate also paid tribute to the four players who will now leave his squad, while the rest prepare to fly out for the Toulon Tournament which starts later this week.
Tom Ince, Danny Ings, Carl Jenkinson and Jesse Lingard all miss out on the trip to France as they’re too old for the competition, but were all involved from the start on Monday.
And they have all played an important part in Southgate’s first season in charge, for which he was keen to single them out for.
"We leave a couple of the boys behind and I must pay tribute to Danny Ings, who’s had an excellent season and I thought Jesse Lingard was outstanding for us," he added.
"He played the number ten role, with and without the ball, exceptionally well.
"Tom Ince has had a really good season for us and Carl Jenkinson, for me, epitomised the group in terms of what they’re like to work with.
"He decided to forego all of Arsenal’s Cup Final celebrations and was adamant that he wanted to play for England and finish the season with us which is an outstanding sign of his commitment."
One sour note for Southgate was the injury sustained by substitute Harry Kane, who will now miss the Toulon trip with an ankle injury.
The Tottenham Hotspur striker came on in the later stages of the game, but was helped off minutes later after suffering the knock.
"It’s a real shame because Harry has been extremely patient for his chance and I was looking forward giving him some of the prestigious games in Toulon," said Southgate.
Watch the full interview with Southgate in the media player at the top of the screen.
"He’s warranted that opportunity and has had a super finish to the season with Tottenham so it’s disappointing for us and for him."