For the champs Manchester City, though, there's still plenty of work to do.
Forest, who many might have thought would be battling relegation this season in the Premier League, moved just a point behind second-place Arsenal by beating Ipswich 4-2 on Saturday.
More importantly perhaps for Forest, the gap to City grew to six points after the soon-to-be-deposed champions drew 2-2 at home to Brighton.
City are hanging onto fifth place, which is likely to be the final Champions League qualification position from the Premier League for next season.
Pep Guardiola's champs twice took the lead in the first half at Etihad Stadium, through Erling Haaland's penalty and Omar Marmoush's fierce shot from outside the box, but they were pegged back each time by opponents who are also in contention to get into the Champions League.
An own-goal by Abdukodir Khusanov in the 48th minute ultimately clinched a point for Brighton, who are only a point behind City.
That meant City have now conceded 40 league goals this season, their most in any single campaign under Guardiola.
"That's because of something missing," said Guardiola, who acknowledged that he could sense a nervousness in the crowd.
"Yes definitely," he said. "Everybody feels the pressure."
Anthony Elanga scored twice for Forest, whose other goals came from Nikola Milenkovic and Jota Silva in the latest win on their march back to Europe's top competition.
Forest famously won the European Cup in 1979 and '80 under Brian Clough and are close to returning to the competition under Nuno Espirito Santo, who had to steer the team away from relegation danger after being hired midway through last season.
Nuno wasn't getting carried away, though.
"You know what I think about the table," he said.
"What we have to do is to focus on ourselves, focus on ourselves. Work as much as we can because there is a lot of football to be played yet."
Ipswich, in third-to-last place, dropped nine points adrift of safety after Wolves — the team directly above the relegation zone — won 2-1 at last-place Southampton. Jorgen Strand Larsen scored both of Wolves' goals.
Leicester, who are tied for points with Ipswich in 19th, host Manchester United on Sunday while Southampton are destined for the drop a further eight points back.
Bournemouth had been another unheralded team in contention for Champions League qualification but they're starting to fade, dropping to ninth with a 2-1 home loss to Brentford.
They haven't won any of their last four league games - or five in all competitions - though they're still only four points behind Man City, their FA Cup quarter-final opponents at the end of the month.
Everton scored in stoppage time through Jake O'Brien to salvage a 1-1 draw at home to West Ham.
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