Referee Andrew Madley disallowed a goal for West Ham against Chelsea after being told to look at the pitchside monitor by VAR
The decisions denied Newcastle United and West Ham goals against Crystal Palace and Chelsea, respectively.
Both teams thought they had scored, with the goals confirmed by the on-pitch referee.
But in each instance the goals were disallowed after VAR.
The decisions have been heavily criticised, with many arguing that the role of VAR is not to reverse debatable calls that have already been made.
The Premier League is to now review the decisions with the PGMOL as a matter of priority.
BBC Sport understands the PGMOL (Professional Game Match Officials Limited) will fully co-operate and collaborate with the Premier League's request, using the outcome as part of an ongoing assessment of weekly performances and the development of its match officials going forward.
West Ham were denied a 90th-minute equaliser when Maxwel Cornet's effort was ruled out after Jarrod Bowen was judged to have fouled Edouard Mendy in the build-up - a decision David Moyes called "scandalous".
"The goalkeeper comes to take it, and actually fumbles it out of his hands five or six yards, so he could never recover it," said Moyes, who added he was "embarrassed" for VAR official Jarred Gillett. "Then he acted as if he had a shoulder injury. I'm amazed that VAR sent the referee to see it.
"It was a ridiculously bad decision. I'd question VAR as much as the referee, but the referee should have stuck to his own guns - there is no excuse for that not to be a goal, none whatsoever.
"The sad thing is this is the level of the weak refereeing at the moment."
Meanwhile, Newcastle saw what manager Eddie Howe called a "perfectly good goal" chalked off against Palace.
Palace defender Tyrick Mitchell turned the ball into his own net and referee Michael Salisbury ruled it out for a foul by Joe Willock on goalkeeper Vicente Guaita, though Newcastle felt the midfielder was himself pushed by Mitchell.
BBC Sport pundit Alan Shearer said: "It is shocking, abysmal, disgraceful - Willock is going to head that ball, so Mitchell shoves him. Michael Salisbury gets it right, it is Lee Mason [VAR official] who somehow bizarrely tells him 'you have made a howler'.
"Lee Mason is the one to blame because it is an inexperienced referee. At this level you have got to get that decision right, he has had no help from VAR. Far too many errors, VAR is not the problem, it is the people who are running it."
World Cup referee Michael Oliver ignored the advice of VAR in a game between Nottingham Forest and Bournemouth at the City Ground, despite being asked to review a penalty decision on the pitchside monitor.
Instead, Oliver opted to stick with his initial call and award Forest the spot-kick for handball.
Elsewhere, Leeds boss Jesse Marsch was sent off for his reaction to two penalty decisions that did not go his side's way in a defeat by Brentford.
-- Courtesy of BBC Sport