The 19-year-old winger is the latest star from Southampton's formidable academy and took just 43 seconds to get the home fans cheering his name after scooping the ball on for Charlie Austin to head in the game's only goal from close range.
Sims had been told he was playing by manager Claude Puel only just before kickoff but showed no nerves in a man-of-the-match performance.
"It was everything you wish for as a kid. Coming through the academy and hearing the crowd call my name is a dream," said Sims, who last Monday was playing in front of a few spectators for Southampton's under-23 side.
Of his part in Southampton's goal, he said: "I just turned and hit it and luckily Charlie was there."
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It was a spectacular start for a side who had failed to muster a single shot on target against Liverpool the previous week, and Sims almost doubled the score with a header when unmarked on the six-yard line before the break.
Once again Everton, who have won only once in eight Premier League games, were punished for starting badly, leaving manager Ronald Koeman struggling for excuses on his first return to the club he left in the summer.
"Sometimes it is difficult to explain why we start badly, said Koeman, who said he had never heard of Sims in his time at Southampton.
"We gave the ball away after 10 seconds and did not defend too well in the area. Southampton had their chances to kill the game but I can't complain about the second half."
Southampton should have extended their lead after the break when Austin was denied by a flying save from Maarten Stekelenburg and James Ward-Prowse blasted one chance wide and had another cleared off the line.
"It was a very good performance for us because we had a lot of injury problems before the match," said Puel.
"Josh Sims -- for his first Premier League game, I guess it's okay! I think it's important to respect the academy here and when we have problems with injuries it's fantastic to be able to start players from the academy."
(Reporting by Neil Robinson; Editing by Clare Fallon)
