Coming into the game, Bremen hadn't won a game yet this season in the Bundesliga and that run continued on as the visitors took the lead five minutes before half-time through Gregoritsch, before Alfreð Finnbogason doubled the lead from the penalty spot.
Gregoritsch then added a third goal just after the hour mark and from their the three points were sealed as Alexander Nouri's men were booed off the pitch once again by the home fans as they failed once again to get their opening win of the league campaign.
Pavlenka kept the hosts' in the game with some impressive saves early on
Despite having lots of possession in the first half, the hosts struggled to break down a resolute visiting defence. At the other end though, it was a different story as the visitors did have chances to score early on but were denied by Jiří Pavlenka.
Pavlenka firstly denied Finnbogason with a brilliant fingertip save after the striker was played in on goal. Pavlenka then denied Cauiby from the edge of the box after the winger hit a powerful shot towards the goal.
Marvin Hitz had only one real save to make in the first half as he denied the returning Max Kruse with a great diving save after the striker unleashed a good strike from the edge of the box.
The visitors though continued to be on the front foot and they came within inches of taking the lead when Daniel Baier unleashed a fantastic shot from the edge of the box and with the keeper beaten, the ball came back off the bar.
Gregoritsch finally gave the visitors' the lead that their play deserved
The breakthrough did finally come for the visitors though soon after when a great cross from Philipp Max found Gregoritsch in the box and the big striker guided a good header into the back of the net.
Just as the hosts' thought that they were going to go into the break only one goal down, the visitors were awarded a penalty in first half stoppage time when Niklas Moisander fouled Finnbogason in the box and after consultation with the VAR system, referee Sören Storks pointed to the spot.
Finnbogason added a second in first half stoppage time from the penalty spot
Finnbogason himself stepped up to take the penalty and he calmly sent Pavelnka the wrong way to double the visitors' lead at the break, while the hosts' knew that they had to improve in the second half in order to get something from the game.
The hosts' started strong at the start of the second half but the visitors scored a third goal on the break
There was a reaction from the hosts' at the start of the second half as they pinned they pinned their visitors' back into their own box but once again some brilliant defending from Manuel Baum's men stopped them from scoring.
It was from this brilliant defending that they scored a third goal on the break when Cauiby received the ball at the halfway line before running a long way before playing a great through pass to Gregoritsch, who made no mistake with the finish by blasting the ball home into the back of the net just after the hour mark.
The visitors' missed further chances as the game ended with loud boos from the hosts' fans
It really should have been more for the visitors as Rani Khedira missed two easy chances when he was through on goal but on both occasions he put his shot off target when he should have done much better.
They didn't though as the game ended with only a three-goal defeat which really will pile more pressure on the hosts' manager Nouri but for the visitors this result will give them hopes for the upcoming games.