The Battle at Mar-Vell's Laboratory was the altercation between a surviving group of Skrulls hiding in Planet C-53s orbit, and a Kree offensive including the Starforce. The battle was initially a chase for the Tesseract, where the stakes later escalated when Accuser Warships arrived to bombard C-53's surface with Kree Ballistic Missiles. Captain Marvel stopped the bombings and neutralized all members of the Starforce, and finally Yon-Rogg in the Mojave Desert, while the Skrulls escaped down to Louisiana for temporary refuge.
After Vers remembered part of her past memories, she realized that Skrulls are the victims of Kree's oppression, and decided to help them escape from the Kree. In order to do that, Norex modified their Quadjet to be able to launch into orbit, where Mar-Vell's Laboratory was located. He then remained on Earth to stall Yon-Rogg, who saw through his disguise and executed him.
Chase for the Tesseract
Carol Danvers, Nick Fury, Maria Rambeau, Talos and Goose arrived at Mar-Vell's Laboratory, but they were ambushed by Starforce, who sent Danvers to commune with the Supreme Intelligence, imprisoned the Skrull refugees and decided to dispose of Fury and Rambeau. But before they could, Danvers overpowered the Intelligence in a mental battle, managed to break free from it and the Photon Inhibitor, and asserted control over her full range of cosmic powers. In the process, she caused the cells where the Kree were keeping the Skrull refugees to overload, giving them a chance to escape.
Danvers retrieved the Tesseract and decided to give it to Fury. He refused to touch it but Goose swallowed it. Danvers then stalled Starforce by letting them think she had the Tesseract, causing an all-out battle between Danvers and her former teammates and allowing the Skrulls, Fury, Rambeau and Goose to escape in a Quadjet. Yon-Rogg, in rage after Danvers defeated all of her former teammates and having lost the Tesseract, authorized Ronan the Accuser and the Accusers to launch Kree Ballistic Missiles at Earth. He and Minn-Erva then embarked on space pods to follow the Skrulls to Earth. Danvers damaged Yon-Rogg's pod, causing him to crash, and destroyed the incoming Ballistic Missiles. Ronan sent more forces to battle danvers but she destroyed all of them along with one of the Accuser Warships accompanying him, forcing him to retreat. On Earth, Minn-Erva tracked down the Quadjet carrying Skrulls, but Rambeau defeated her in air combat, destroying her pod and killing her. Danvers arrived on Earth and faced Yon-Rogg once more.
Duel in the Mojave Desert
After defeating the Kree armada, Danvers went back on Earth to the Mojave Desert to face Yon-Rogg, causing nearby power grid lines to overload by her mere presence near them. Yon-Rogg admitted that he admired her progress since when he had first met her, and invited her to a 'fair' fight without using her powers to prove herself to him. Danvers, not going by the rules of her former boss anymore, simply incapacitated him with a photon blast, stating that she had nothing to prove to him. She then put him back in his still functioning pod to send him to Hala with a warning message to the Supreme Intelligence.
As the Kree forces attacking Earth were defeated, the remaining Skrulls gathered in Rambeau Residence for temporary refuge, along with Danvers and Fury. Danvers agreed to finish what Mar-Vell had started and help the Skrulls find a new home away from the Kree. Suffering a defeat at the hands of Captain Marvel, the Kree Empire became aware of a new security force protecting Earth. Although Ronan the Accuser claimed they would come back for Danvers, he failed to deliver that promise as the peace treaty between the Kree and Xandar caused him to defect from the Kree, and later be killed by the Guardians of the Galaxy.