It came last April in what was only the fourth-all Yorkshire FA Cup semi-final when Baxter put the Blades ahead against Hull City with a close range finish after 19 minutes.
Wallace, then a Tranmere Rovers player, was inside the national stadium that Sunday, cheering on his fellow Merseysider, so when the ball hit the back of the net he admits to being overjoyed.
Hull, of course, hit back to win a thrilling tie 5-3, but Baxter, quite rightly, is still proud of being the first Blade to score in three visits to the rebuilt Wembley.
United are back on the Cup trail again tonight, a place in the Capital One Cup quarter-finals being at stake when Nigel Clough takes his men to Milton Keynes Dons.
“I would love to do what the lads did last season,” said the 22-year-old when asked about the South Yorkshire club’s exploits in knockout football last term.
“I went to the semi-final to watch Jose. For me, as a neutral, it was a fantastic day out and I would love to be involved in something like that.
“Those are the sort of days you want as a player. I left Everton because I was not going to be a regular and I want to have things in my career that I can look back on proudly. You want achievements to look back on.”
Asked if Baxter was fond of mentioning last season’s Cup run during their drive to Sheffield every day for training, a smiling Wallace replied: “He is always on about scoring at Wembley.
“He throws it in all the time – and how he was the first Sheffield United player to score at the new Wembley.
“Seriously, though, it is a great achievement and it would be great if we could get through against MK Dons to land another big tie.”
United’s run to Milton Keynes began with a 2-1 home win over Mansfield Town, but it was the penalty shoot-out win at West Ham United in the second round that truly evoked memories of last season.
Wallace came off the bench in extra-time at Upton Park and he then started in the next round as a return to the East End brought a 1-0 victory over Leyton Orient.
That triumph at Brisbane Road came just three days after Clough’s men had crashed 5-2 at Swindon Town, but their form since then has been impressive with six league games having yielded 13 points. Hartlepool United have also been disposed of in the Johnstone’s Paint Trophy.
“There are signs we are knitting together,” said Wallace, who was one of a double figure total of new arrivals at the Lane in the summer. “The performances are coming. We are passing teams off the park, we just need to score more goals.
“If we can get that right, we will be fine. Hopefully, it will happen in the next couple of games.
“Everyone is getting chances. It was good to see Stefan Scougall opening his scoring account on Saturday (in the 1-0 win at Crewe). We need everyone to chip in with goals, not just the forwards.
“I am hoping the goals will come for me with games. I am getting in the box, but the ball isn’t quite falling.”
A first goal in United colours tonight would, of course, be timely for a player who returned to action at Gresty Road after missing the previous two games with a groin problem.
He said: “I was happy to play 101 minutes, with all the stoppage time there was. I got a bit of cramp, but it was great to be out there.
“I haven’t played a lot of football in the last two years so I am happy just to be out there and playing a full game.
“It was great coming back into a winning team. They had done brilliantly without me, winning one game at home and another away. So, I was surprised to be back in the team.”
As for the League Cup, Wallace added: “If we beat them we are more or less guaranteed a big tie in the next round. We would be in the last eight and it would be great to get a big home tie at Bramall Lane.
“We have not had it easy in the competition so far. West Ham was a big, big result. We took a lot of confidence from that and while drawing a team from your own league is not a great thing, hopefully we can get through.
“This is a big club. We have not been talked about that much but I get the feeling that people are starting to be aware of us. We are doing our business quietly and people are starting to worry about us now. That is great for us.
“That is a different feeling for me. At Tranmere, we sort of worried about the opposition and how they might play. But here it is the other way round and I like that.”
Last six games: Milton Keynes Dons LWLWDW, Sheffield United LWDWWW.
Referee: R East (Wiltshire).
Last time: Milton Keynes Dons 0 Sheffield United 1; March 1, 2014; League One.