Scott Robertson scored in the 21st minute and Dundee United beat Scottish Premier League champion Celtic, 1-0, on Sunday at Tannadice Park.
Robertson reached a cross from Paul Dixon to head home the lone goal, also on the only shot for Dundee in the match. Dundee is fourth in the table, and four points clear of Hearts entering the final week of the season.
Dundee has clinched a Europa League place, as Rangers will not be eligible for European competition next season.
Celtic, which is 20 points clear of Rangers at the top of the table, clinched the league title and a Champions League berth weeks ago. The Bhoys wrap up the season at home against Hearts next week.
Dundee concludes its season at Motherwell.
Hearts 2, St. Johnstone 0
Edinburgh, Scotland - Rudi Skacel and Andy Webster scored as Hearts downed St. Johnstone, 2-0, on Sunday at Tynecastle Stadium in the Scottish Premier League to close in on a Europa League berth.
With Rangers ineligible for European play next season, Hearts needs to finish fifth to make the Europa League. Hearts moved from sixth to five with the win, two points ahead of St. Johnstone entering the final week of the season.
St. Johnstone will need a home win against Rangers next week to earn fifth and hope Hearts fails to pick up a point at Celtic.