Sakala strikes as Rangers win again under new boss Beale
Victory left Rangers in second place but still a huge nine points behind leaders and reigning champions Celtic, their arch-rivals.
Dundee United started brightly at Tannadice but two goals in three second-half minutes decided the game.
Zambia striker Sakala burst into the box and shot high into the net past Mark Birighitti in the 54th minute.
Malik Tillman doubled the lead after the goalkeeper had initially saved from Sakala, with this result leaving Dundee United 11th in the 12-team table - behind Motherwell on goal difference - after a first defeat in four league games.
Earlier, Kevin Nisbet scored a hat-trick as Hibernian won 3-2 away to Motherwell in a result that eased the pressure on manager Lee Johnson.
Scotland striker Nisbet, only recently back in action after 10 months out with a cruciate ligament injury, was in fine form as Edinburgh club Hibs enjoyed a much-needed win following a run of nine defeats in 11 matches to move up to seventh in the table.