Rangers has one game left to complete Scotland’s unbeaten Premiership campaign after being beaten by Livingston.
Ryan Kent finished one with Alfredo Morelos by tapping the visitors’ second and Hagi hitting the third.
Scott Pittman and Jaze Kabia hit the woods with Livi’s good chances.
Steven Gerrard’s Rangers set Scotland’s new record of clean sheets in the 38-game season 25. Will receive the Premiership trophy after Saturday’s home game against Aberdeen.
Livingston remains in contention to jump over his next rivals St Johnstone in fifth place. The sides are level on points, and the Saints are two better goals.
Jay Emmanuel-Thomas upset the Rangers early on, creating a space for Josh Mullin to save Jon McLaughlin.
Hagi and Kent fired a wide shot into Livingston’s goal before the first half of the first half.
Kemar Roofe threw Hagi the ball after defense in Livingston. And the Romanian played the ball before colliding with Stryjek.
Referee Don Robertson took it as a mistake, despite protests that Hagi had thrown the ball out.
Having missed his last three penalties, Tavernier moved up to the goalkeeper’s right, his 19th goal of the season.
And the club captain himself was involved in the second goal and his ball in getting Kent high.
The rangers tried to sacrifice Morelos.
The ranger tried to sacrifice Morelos but forced the striker to ignore them and get a return pass to finish.
And the Livingstons were a few inches from dividing their faults in two.
The Pittman’s shot shook the bar, and the Ranger goalkeeper Jon McLaughlin forced the ball clear. Under pressure from a chasing paper.
And after that, Kabia received a good chance after the cross by Nicky Devlin, a forward player who could hit the left-back.
Joe Aribo tested Stryjek after a while, and Kabia was not where he got headed when he clung to another Devlin delivery on the other side.
Ranger finished scoring with a quick move to the left, Cedric Itten replacing Roofe, sharpening Hagi’s squad to inflict a brutal blow.
What did we learn?
Livingston’s 14 games of unbeaten 14 games have seen them finish their top half match. But Livingston has only won once since the series ended in early February.
Emmanuel-Thomas appears to be attacking. But he needs more support from a wide range if Livingston ends the season-high.
Among the injuries and the inclusion of other players, the Ranger counted only six players. And full-backs Aribo who played a rare role at left-back.
He looked far-fetched, but there was a deliberate tourist plan. To attack the other side with Tavernier, Kent, and Hagi, a simple tactic that they were managers.
What did they say?
Livingston manager David Martindale: “We are very disappointed. I am delighted with the performance of the spells in this game. Ranger has been very clinical in our box.
“We had enough chances to take something in this game. We hit the bar, hit the post, and got another chance.”
Rangers manager Steven Gerrard: “Tonight we can get a clean record. And Saturday gives us a chance to break 100 points, which will be a fantastic league campaign.
“Our home record has been strong. We need to make it to the finals now.”