His Yorkshire team-mates Dan Brown (Masham) and Will Whiteoak (Shipley) delivered a win and a half respectively in the afternoon as England came back from a 3-2 foursomes deficit to triumph 9.5-5.5.
Hague’s opponent Llewellyn Matthews conceded a putt on the 12th green to give the Yorkshireman an 8&6 win with a five-under-par performance.
England had beaten Scotland 9-6 on day one and share top place with Ireland, who followed a 9-6 defeat of Wales with a 10-5 victory against Scotland.
Ireland are looking to win the Raymond Trophy for the fourth year in a row while England are hoping for their first victory since a previous triumph on Yorkshire soil, at Ganton in 2013.
England were grateful to be only a point in arrears against Wales after the foursomes when a battling finish, featuring three of the team’s new caps, kept them in touch.
Jack Gaunt and Hague, who are both making their debut at this level, continued their 100 per cent foursomes record with a 3&1 win.
Experienced Bradley Moore and new cap Jake Burnage came from one down after 15 to win on the last.
In the afternoon singles Wales led early in the top two matches, but the other eight England players were all ahead as they went through five holes. It looked even better for the hosts when Gian-Marco Petrozzi clawed back his early deficit and reached the turn all square.
Hague drew England level with his overwhelming win, and Petrozzi and Brown both won their games to edge England ahead.
Back came Wales, with Whiteoak and new English men’s amateur champion Todd Clements both being pulled back to all square, while Gaunt and Moore fell behind and only Josh Hilleard and Jake Burnage were up.
But it was on the 18th green that England would see matters swing their way. Whiteoak and Clements both avoided defeat when their respective opponents missed makeable putts that would have given a huge boost to the Welsh cause.
Burnage, playing as anchorman, closed out his game 5&4 and left the way clear for Hilleard to clinch the win on the 17th.
“I didn’t realise it was for the win, but when I saw the scoreboard on the 16th tee it looked like a halved match and so I knew my point was needed,” said Hilleard. “Going into the singles behind we needed to press and the guys have obviously done it. Everyone will be happy and ready (for Friday’s match).”
The overall result became more decisive when Gaunt won the 18th to square his match and Moore won one up.
Team captain Kevin Tucker praised his new caps, saying: “They all collected points in the singles when the chips were down.
“(Friday) will be a good game. Ireland are the strong favourites with a very experienced side, but our young players are looking forward to the challenge facing them.”
Ireland made no mistake against Scotland. They had a 4-1 advantage after the foursomes and went on to win six of the 10 singles.
The defending champions hold a slender advantage over England in terms of games won, which will be in their favour should Friday’s match be halved.
Wales and Scotland will play-off for third place.