* Kompany scores as Man City down Southampton 3-0
* None of the clubs in the bottom six managed a win. (Adds City victory)
LONDON, April 15 (Reuters) - Tottenham Hotspur remained a worrying presence in Chelsea's rearview mirror after a second successive 4-0 victory cut the gap in the Premier League title race to four points on Saturday.
Bournemouth became the 12th consecutive side to leave White Hart Lane empty-handed as Harry Kane hit the 20 league goal mark for the third season in a row with his side's third.
Long-time leaders Chelsea are away at Manchester United on Sunday for what looks the toughest fixture of their run-in.
"We got the three points and now the pressure is on Chelsea to win in Old Trafford," Tottenham manager Mauricio Pochettino said. "It would be fantastic if tomorrow night, after the game, the gap is still four points. But four points is still a lot."
With only two of their last six matches at home Tottenham are still rank outsiders to snatch a first title since 1961.
Kompany's impassioned celebration, following his 55th-minute opener, told the story of what has been two injury-hit seasons for the inspirational Belgian defender.
"I don't really complain about what's happened to me, I just carry on," Kompany, whose goal was his first since August 2015, told BT Sport.
"When this happens I feel I'm giving something back to the fans. I'm finally giving something back to the team and that's what you see in that moment."
Leroy Sane and Sergio Aguero -- with his 11th goal in 11 games in all competitions -- were also on the scoresheet.
In the title run-in, Chelsea must still also visit Everton who racked up an eighth successive home win when beating Burnley 3-1 to move above Arsenal and United into fifth, albeit having played more games than the teams around them.
Premier League top scorer Romelu Lukaku struck Everton's third, taking his season tally to 24.
There was little movement in the relegation battle with none of the clubs in the bottom six managing a win.
Bottom club Sunderland scored their first goal in eight games as Fabio Borini's late equaliser earned them a 2-2 draw at home to West Ham United which left them nine points behind 17th-placed Hull City who lost 3-1 at Stoke City.
Second-from-bottom Middlesbrough host seventh-placed Arsenal on Monday while 18th-placed Swansea City slumped to a fifth defeat in six matches in a 1-0 loss at Watford.
Swansea remain two points behind Hull while Crystal Palace, who battled back from two down to draw 2-2 at home to champions Leicester City, are seven points above the relegation trapdoor.
Bournemouth are still looking over their shoulders, although they also have a seven-point cushion.
Since losing to Liverpool on Feb. 11 Tottenham have won seven games in a row -- their best top flight sequence for 50 years -- scoring 22 and leaking only four.
A week after beating Watford 4-0, having also kicked off before Chelsea, they produced another display oozing confidence with Mousa Dembele and Son Heung-Min scoring inside the first 20 minutes and Kane striking just after halftime.
Kane is the fourth player to score 20 or more goals in the Premier League three seasons in a row, joining Thierry Henry, Alan Shearer and Ruud van Nistelrooy.
"Sometimes it's good to play first. Early kick off, get the three points and then we can enjoy our Easter weekend and see what happens tomorrow," Kane said.
"Hopefully Man Utd can get a result for us."
Three days before taking on Atletico Madrid in their Champions League quarter-final, seeking to overturn a 1-0 deficit from the first leg, Leicester were involved in a rip-roaring duel at Selhurst Park.
Goals by Robert Huth and Jamie Vardy put them 2-0 ahead but Palace hit back through Yohan Cabaye and Christian Benteke.
(Reporting by Martyn Herman and Tom Hayward; Editing by Toby Davis)