Walcott scored shortly after coming on as a substitute and then set up Danny Welbeck for a sublime winner as England rallied for an entertaining 3-2 win over Sweden on Friday.
The result eliminated Sweden from the European Championship and put England on course for the quarterfinals. The English only need a draw against co-host Ukraine in the final group game to advance.
"Just to make my first appearance in such a high-profile arena it just means so much to me," Walcott said. "It's been a long time waiting and hopefully there'll be more to come from me."
Walcott was overlooked for his younger Arsenal teammate Alex Oxlade-Chamberlain in England's opening game of the tournament, only coming on in injury time, and again began on the bench on Friday in favour of James Milner and Ashley Young. But after England wasted a halftime lead to fall behind 2-1 against a Sweden team desperate for a victory, coach Roy Hodgson turned to Walcott in the 61st minute.
Three minutes later, Walcott had put England level with a swerving shot from distance after a corner was headed out to the speedy winger outside the area.
He followed that up by breaking into the area and sending a low cross to Welbeck, who flicked a backheel past a diving Andreas Isaksson in the 78th to give England its first win over Sweden in a competitive game in eight tries.
"It was a very clever finish," Hodgson said. "It was goal worthy, in my opinion, of winning the game."
England gets Wayne Rooney back in the next game after a suspension, but with Walcott and Andy Carroll both putting in strong performances, Hodgson will a tough decision as to who will be on the bench.
"We all know the ability Theo has got and that's the same right across the squad, so whoever comes on the pitch is going to make a difference," Welbeck said. "I'm very happy for Theo."
After a 1-1 draw against France, Friday's victory may silence some of the critics who thought England had become too defensive-minded under Hodgson as it proved that it can score goals when it needs to.
"We felt, from the first game, that we wanted to pick it up a bit more offensively," Walcott said. "And if you score three goals that's the main thing."
Sweden, for its part, let a second-half lead slip away for the second game in a row after falling 2-1 to Ukraine in its opener. While the Swedes put in a much-improved performance on Friday, they once again failed to shut their opponents down defensively.
"I thought we were a much better team than them," Sweden captain Zlatan Ibrahimovic said. "We've taken the lead in two games now after 60 minutes and then lost it. ... But today we played exactly the way we want to play."
In a game that featured plenty of chances for both sides, Carroll had given England the halftime lead with a powerful header in the 23rd minute that showed exactly why Hodgson elected to start the tall Liverpool forward up front. Carroll got between two defenders to meet Steven Gerrard's cross into the area as Sweden was once again exposed in the air.
But Sweden fought back through an unlikely source in Mellberg, whose shot past Joe Hart was pushed into the net by Glen Johnson. The veteran defender, who has said he will quit international football after this tournament, then rose highest to meet a long free kick from Sebastian Larsson to put the Swedes ahead in the 59th.
"It was a cracking game of football," Hodgson said. "We were reasonably comfortable at halftime and had a good control of the game before they rocked us on our heels."
But Walcott then started the English comeback when a corner was headed out to the Arsenal winger outside the area and his shot wrong-footed Isaksson, who was falling the wrong way and flailing with his arms as he watched the ball fly into the middle of the net.
"They were much more effective than we were," Sweden coach Erik Hamren said. "I'm really proud of the players. We showed the mentality and the attitude I wanted to see. ... But to win games you need also a little bit of luck."
Sweden: Andreas Isaksson, Andreas Granqvist (Mikael Lustig, 66), Olof Mellberg, Jonas Olsson, Martin Olsson, Anders Svensson, Kim Kallstrom, Sebastian Larsson, Rasmus Elm (Christian Wilhelmsson, 81), Zlatan Ibrahimovic, Johan Elmander (Markus Rosenberg, 79).
England: Joe Hart, Glen Johnson, Ashley Cole, Steven Gerrard, John Terry, Andy Carroll, Ashley Young, Joleon Lescott, James Milner (Theo Walcott, 61), Scott Parker, Danny Welbeck (Alex Oxlade-Chamberlain, 90).