United took a seventh-minute lead through Patrick Bamford and after both sides had hit the post, Leeds doubled their advantage five minutes before the break through a stunning direct free-kick from Phillips.
Rovers then pulled a goal back three minutes after the break through another impressive free-kick from Adam Armstrong but Mateusz Klich's drive restored United's two-goal cushion five minutes later.
With five games left, the victory pushed United four points clear of second-placed West Brom who host Hull City on Sunday with Leeds remaining six points clear of third-placed Brentford who recorded a fifth-straight win with victory at home to Wigan Athletic as Said Benrahma bagged a hat-trick.
Rovers threatened in the second minute after Leeds gave away possession but Illan Meslier safely held former Whites midfielder Bradley Johnson's fierce drive.
Leeds then went close soon after when a neat cross from Ben White flew through the area and behind for a goal kick.
And after just seven minutes United took the lead when Mateusz Klich robbed Lewis Travis of possession and provided a simple through ball for Patrick Bamford who easily fired home from just inside the box.
United were looking good and again opened Rovers up two minutes later with Klich unable to finish off the attack but the Whites were given a huge let off in the 11th minute when Sam Gallagher was played in one-on-one but pulled the ball the wrong side of Meslier's right-hand post.
Meslier then came to the rescue seconds later by smothering the ball at Adam Armstrong's feet before Bamford's control let him down when through at the other end.
But Rovers were then inches away from equalising in the 13th minute as Gallagher fed Lewis Holtby whose strong drive crashed back off the post.
As part of a frantic opening, Tyler Roberts then saw a shot blocked from a tight angle and Rovers then lost Elliott Bennett to injury in the 22nd minute.
United then began to control possession and from a lovely, intricate move, Bamford was only denied a second by the post with a curling shot from inside the box.
Back came Blackburn with Joe Rothwell curling an effort just over the bar but fantastic work from White then worked an opening for Jack Harrison whose cross was cleared.
From the resulting corner, Luke Ayling's flick hit the post and Roberts was then hacked down on the edge of the area as Rovers looked to clear.
Up stepped Phillips, and the Whites midfielder produced a majestic strike from 20 yards that flew into the top left corner to double United's lead and give the Whites a 2-0 advantage at the break - with skipper Liam Cooper surviving an awkward landing on his back just before the end of the half.
Leeds looked to be cruising but Blackburn pulled a goal back three minutes with Adam Armstrong this time converting a peach of a free-kick after referee Robert Jones had harshly adjudged Phillips to have fouled.
Ayling then curled a cross wide at the other end before Rovers saw appeals for a penalty waved away after Gallagher was sent tumbling.
But United then restored their two-goal cushion in the 53rd minute when Harrison's shot was rebounded back into the path of Klich whose shot from the edge of the box flew under 'keeper Walton.
After lovely play from Barry Douglas, Ayling then headed wide before Roberts saw his shot blocked.
Pablo Hernandez was then introduced for Roberts on the hour, shortly after another Ayling cross had whistled past the post.
United continued to pour forwards in search of a fourth goal and Rovers were extremely fortunate to see 'keeper Walton only handed a yellow card for taking out Bamford when through on goal on the edge of the box.
Walton saved Douglas' free-kick but the Leeds onsluaght continued with Cooper heading just wide from a Phillips free-kick before Bamford's shot was blocked after a delicious chip from Hernandez.
Blackburn somehow held firm without conceding a fourth but the damage had been done with United now needing ten points from their final five games to guarantee automatic promotion, even if Brentford win every remaining game.
Blackburn Rovers: Walton, Nyambe, Lenihan, Adarabioyo, Bennett (Downing 21), Rothwell (Buckley 68), Travis (Davenport 68), Johnson, Gallagher (Graham 60), Holtby (Samuel 60), Armstrong. Subs not used: Leutwiler, Chapman, Mulgrew, Carter.
Leeds United: Meslier, Ayling, White, Cooper, Douglas, Phillips, Klich (Shackleton 88), Harrison, Alioski, Roberts (Hernandez 61), Bamford. Subs not used: Miazek, Davis, Stevens, Berardi, Gotts, Poveda, Struijk.
Referee: Robert Jones.