Wayne Rooney says it was a "special moment" to score the winning goal on his top-flight return to Everton after 13 years and one he has been looking forward to for a long time.
The 31-year-old, who left the club for Manchester United in 2004, headed in his 199th Premier League goal as the Toffees beat Stoke 1-0 at Goodison Park.
Rooney said a lot of "relief and emotion" came out as he celebrated what proved to be the decider before half-time.
"On a personal note, I'm absolutely delighted to score the winning goal at Goodison Park," he told BBC Sport.
"It was a special moment for me.There was a lot of relief and a lot of emotion.It was an important goal just before half-time.
"I've felt at home since I first stepped in the training ground.I've been looking forward to this moment for a long time."
Rooney found space in the area to head a Dominic Calvert-Lewin cross past Stoke goalkeeper Jack Butland in what was the Toffees' best move of the match - one the former England captain was twice involved in before adding the finishing touch.
Calvert-Lewin also went close for the home side as Stoke struggled to break Everton down on the opening day.
Xherdan Shaqiri's long-range effort did force new Toffees goalkeeper Jordan Pickford into a fine save in stoppage-time, with the 23-year-old leaping across his line to tip wide.
Rooney's perfect homecomingRooney scored 17 goals during his first spell at Everton
Rooney scored the first of his Premier League goals for Everton with a sublime strike against Arsenal as a 16-year-old in 2002.His 199th in the English top flight 15 years later wasn't quite as dramatic, but it will have meant just as much to the boyhood Blues fan.
Sir Alex Ferguson moved to snap up the teenager after some flashes of genius in an Everton shirt and Rooney returned to Goodison Park as England and Manchester United's all-time leading goalscorer.
He helped start the move that resulted in the winning goal with some neat link-up play with Idrissa Gueye and Sandro Ramirez, before showing all that experience to peel away in the area and guide a free header into the opposite corner.
The forward started tenaciously and could have found himself in the book for a late tackle on former United team-mate Darren Fletcher, but Rooney's desire to track back and help his side defensively also proved invaluable against a direct Stoke threat.
This season could go a long way to deciding his legacy among the Everton faithful, but the former England captain will also be hoping to play his way back into Gareth Southgate's plans with a World Cup looming next summer.
The winning goal on his Goodison Park homecoming proved a perfect start.
How did the new signings fare?Kurt Zouma has joined Stoke on a season-long loan from Chelsea
Everton have spent the best part of £100m this summer, with a club record £50m move for Swansea playmaker Gylfi Sigurdsson potentially still to come before the deadline.
Pickford's late save from a Shaqiri effort that looked to be heading for the top corner will have helped prove his worth as the most expensive British goalkeeper, and the £30m man also instilled confidence in his back three with his commanding presence around the Everton box.
The England Under-21 international was, alongside Rooney, the standout among five new arrivals who started for Ronald Koeman's side.
Stoke, meanwhile, have done most of their business on the cheap.
Kurt Zouma looks a solid acquisition for Mark Hughes' side and the on-loan Chelsea defender stopped Calvert-Lewin doubling the hosts' lead with a superb block in the second half.
The Potters snapped up Scotland international Fletcher from West Brom, and the 33-year-old central midfielder made more passes (45) than any other play on his side while also firing narrowly wide from distance.
Man of the match - Idrissa Gueye (Everton)Rooney's goalscoring return may make the headlines, but Idrissa Gueye was the glue that held together an at times scrappy Everton performance.The Senegal international made more tackles (five) than any other player on the pitch, had the most touches (92) and made more passes than any other midfielder.He even managed a rare shot on target.
'Wayne is one of the best in his position'Everton 1-0 Stoke:Wayne Rooney different class - Ronald Koeman
Everton boss Ronald Koeman said:"The points are really welcome because you don't know what to expect on the first day.It wasn't the performance we like.The team looked nervous on the ball - that's the reason I changed the system at half-time.We need to improve a lot."
On Wayne Rooney scoring the winner:"Wayne showed he is still one of the best in his position.He was very comfortable on the ball and made good decisions on the ball and scored a great goal."
Stoke boss Mark Hughes said:"The story is all about him [Rooney] because he has won the game for Everton.The one man you don't want in those situations is Wayne.
"I'm disappointed with the result but not the performance."
On Jordan Pickford's late save to deny Xherdan Shaqiri an equaliser:"It was fantastic.Obviously Everton have invested a lot of money in their side.There didn't seem a great deal of difference between the two sides."
The stats - 4,869 days between goals
- Rooney set a new Premier League record for the longest gap between two appearances for the same team (4,837 days).
- Rooney also set a new Premier League record for the longest gap between goals for the same club (4,869 days).
- No player has scored more Premier League goals on the opening day than Rooney (eight - level with Alan Shearer and Frank Lampard).
- Rooney's effort was his 300th goal involvement in the Premier League (199 goals, 101 assists), only Alan Shearer (324) has more.
- Mark Hughes hasn't won any of his past seven opening day Premier League games (D2, L5) in charge of three different clubs in that time (Fulham, QPR and Stoke).
- The Potters have failed to score in seven of their past nine away games in the Premier League.
Everton host Hajduk Split in the Europa League qualifying play-offs first leg on Thursday (20:05 BST), before visiting Manchester City on Monday, 21 August (20:00).
Stoke play Arsenal in the Premier League next Saturday (17:30), before welcoming Rochdale in the EFL Cup on Tuesday, 22 August (19:45)....