England were out of the blocks quickest with Will Homer breaking free from 40m for the first try of the match.
England’s powerful Api Bavadra powered over to put his side 14-0 ahead at the break and in control but Wales staged a stunning fightback in the second spell.
Richie Pugh’s side were then reduced to six men when Tyler Morgan was yellow carded for a deliberate knock-on but the Welsh defence held on heroically while they were a man down.
England were left ruing that missed opportunity when Wales hit back with their first try, Morgan Williams sliding into the corner and narrowly avoiding the touchline by the finest of margins to bring Wales to within nine.
The visitors finished with a flourish, Williams with his second exploiting a narrow England defence to score in the corner once again.
But it was too little too late though as England held on to seal a 14-10 win and guaranteeing their place in the 9th place final later in the day.
Wales now have the HSBC World Rugby Sevens Series finale in Los Angeles on 27-28 August to focus on before heading to South Africa for the Rugby World Cup Sevens kicks on 9-11 September in Cape Town.
World Rugby Chairman Sir Bill Beaumont said: “We have had three fantastic days of scintillating, world class rugby sevens in front of huge crowds at Coventry Stadium in what has been another superb showcase for the sport.
“The standard of rugby has been exceptional and congratulations to the medallists who will cherish this moment for years to come. We pay tribute to the Birmingham 2022 organisers for putting on an excellent event in a vibrant stadium and a special thank you to the thousands of volunteers who are the heart of the Games.
“The future of sevens is very bright and we now look forward to an exciting climax to the men’s HSBC World Rugby Sevens Series 2022 in Los Angeles in August, followed by the highly anticipated Rugby World Cup Sevens in Cape Town on 9-11 September, involving 40 of the best teams from across the globe.”