The Swede finished off Dundee United's second-half fightback when he threw himself at Charlie Mulgrew's free-kick with 12 minutes left.
David Goodwillie had given the hosts hope after deflected goals from Anthony Stokes and Mark Wilson put Celtic in command before the break.
Celtic's previous trip to Tannadice had resulted in long-lasting controversy with Dougie McDonald eventually quitting amid the fallout over his false explanation of why he had rescinded a penalty award to the visitors, a furore that played a significant part in the referees' strike.
Extra spice was also added to the occasion by sniping between managers Peter Houston and Neil Lennon, but there was not too much to dispute in their latest encounter as Celtic quickly took control and soon repelled a spirited United revival before securing their fifth consecutive SPL win.
Celtic captain Scott Brown shook off a groin injury as Lennon restored Stokes up front following the Scottish Cup draw with Rangers, with midfielder Ki Sung-yueng dropping to the bench.
Dundee United made one enforced change with Morgaro Gomis coming in for the suspended Jon Daly.
The pitch passed an early-morning inspection following continuing heavy rain and held up well.
Mulgrew saw an early free-kick held by Dusan Pernis as Celtic begin to stamp their authority on the game.
United had an ambitious penalty claim rejected by Mike Tumilty when Majstorovic challenged Craig Conway in the air and Celtic soon took a 16th-minute lead.
Beram Kayal dispossessed Scott Robertson and fed Stokes, who ran into the box before firing a left-footed shot which bounced up off the backtracking Garry Kenneth and inside Pernis' near post.
Prince Buaben soon burst through at the other end but Fraser Forster came off his line to block the midfielder's effort with his feet.
United continued to press with Conway on the left flank their main attacking outlet, but the Celtic defence coped comfortably and the visitors extended their lead in the 35th minute.
Wilson fed Hooper and continued his run before striking Brown's cutback from 14 yards and seeing it go in off Sean Dillon.
The former United player was booked for celebrating with the travelling support, who were almost treated to another first-half goal.
Hooper's cross caused chaos in the United box with Joe Ledley and Stokes both seeing efforts blocked by some desperate defending.
Goodwillie carved out a chance for himself at the other end but fired the ball across the face of goal.
Majstorovic headed a back-post Commons corner just wide as Celtic enjoyed a comfortable opening to the second half.
Danny Swanson soon replaced Gomis as United looked for inspiration and Conway volleyed over the stand when an unconvincing Forster punch handed them a rare half-chance.
But they got back in the game in the 64th minute. Wilson was somewhat fortunate to escape without a second yellow card after fouling Conway near the touchline but Celtic were soon made to pay.
The visiting defence failed to clear Conway's free-kick and Forster parried the ball out as far as Goodwillie, who stabbed the ball into the corner from eight yards.
Goodwillie came close to an equaliser when he turned inside his man after a positive run from substitute Johnny Russell, but Forster got a hand to his powerful low shot from the edge of the box and the ball spun over.
United were now pinning Celtic back but Hooper almost finished them off when he raced on to Dillon's short headed back pass, sliding the ball past the onrushing Pernis but seeing it come off the far post.
Majstorovic did restore the two-goal cushion when he dived on the edge of the six-yard box to head home fellow centre-back Mulgrew's inswinging free-kick after Swanson had tripped fellow substitute Georgios Samaras.
Hooper had two chances to add his name to the scoresheet in the closing stages, but he completely lost his footing six yards out before being flagged offside when converting a low cross from Samaras, who also missed a late opportunity.