But the hosts kept pressing and grabbed the victor in stoppage time when Rose and Livermore went for the ball during a goalmouth scramble and Livermore poked it in to spark wild scenes.
Chelsea can close the gap to two points with a home win over Champions League finalists Liverpool on Sunday, and they face Huddersfield Town and Newcastle United next week, with Spurs hosting Newcastle and Leicester City.
Palace lost its first seven games but is mathematically safe, completing the considerable upturn in its fortunes after Roy Hodgson succeeded Frank De Boer early in the campaign. We've come together and there's been some pride restored and the feelgood factor within the community and within the supporters.
Google celebrates International Labour Day with sketch doodle of tools and implements
One of these was organised at Triplicane Beach and the other one was arranged at the beach opposite Madras High Court. Today, a team of "Doodlers" - illustrators, graphic designers, animators and artists - work on the Google Doodles .
The former England manager has endured mixed fortunes at the club - saving them from relegation but incurring the wrath of the fans with his negative style of football. "I think we are in a good position".
"The important thing for me is that we come together for the importance of the club, if we do that we'll make the right decisions for the future".
Tottenham Hotspur manager Mauricio Pochettino is pleased that the Premier League's top four teams are guaranteed a Champions League group stage spot next season following Arsenal's Europa League exit on Thursday.
He said: "It's great to be nominated with those calibre of managers, it really, really is - I am honoured. It could've been anybody out there".
Oculus' Hugo Barra Unboxes the new Oculus Go
The Oculus Go is a follow-up to the Oculus Rift, but unlike that device it does not require a connection to a computer. The Oculus Go is also designed with a lightweight, breathable fabric so that it can be worn for hours at a time.
Harry Kane was denied by Ben Foster while Erik Lamela and Christian Eriksen were also thwarted by the goalkeeper. They would not only need to win their remaining two games against Tottenham and Crystal Palace, but they would need a fair few results to go their way in other matches too.
Watford will also be playing in the Premier League again next season after a 2-1 home win over Newcastle, which was a first victory in eight games.
Kane will need to score that many to even have a chance of catching Mo Salah in the race for the Golden Boot.
While some might argue that Spurs have little to play for now that they have been knocked out of all the cup competitions, there is still the small matter of finishing in the top four, with fifth-placed Chelsea still on their tails and Liverpool just ahead in third.
Talk of 'hung assembly' by paid agents means Congress defeat: PM Modi
As many as 15 rallies are planned in the state and BJP targetted Congress and they aim to unseat Congress from power. The Union government has put on hold Karnataka government's proposal to approve an official flag for the state.