Sam Groth achieved a treasure trove of firsts in defeating defending champion and fourth seed Nicolas Mahut 6-3, 6-4 in the quarterfinals of the Hall of Fame Tennis Championships at Newport, R.I., this afternoon. The win advances Groth to his first ATP Tour semifinal Saturday, will push him into the Top 100 when the updated rankings come out on Monday and guarantees the Australian direct entry into the U.S. Open main draw in August. Groth, currently ranked a career-high No. 123 in the world, has had an impressive run of results lately, finishing runnerup to Nick Kyrgios in the Nottingham-2 Challenger and qualifying into the Wimbledon main draw, where he lost a first-round match to Alexandr Dolgopolov in three tight sets. The big-serving Aussie has posted a 10-2 overall record on grass during this hot streak. “I’ve got myself in great shape,” Groth said. “I’m not losing my mind out on court. I’m doing a lot of things better. I’ve tightened up my groundstrokes. I’m volleying better than I ever have. I’m making it tough for guys to break me. I’m becoming more prepared to be a top player.” Groth got the only break of first set in the sixth game, and closed it out with an ace on set point. Mahut saved three break points in the third game of the second set, but double-faulted on the fourth to gift Groth the game. That was all Groth needed, as he erased the only break point of the match against his serve in the eighth game, and held steady the rest of the way, punctuating the win with an overhead smash on match point. “[Groth] played well today. I have to congratulate him,” Mahut said. “He was too good and too consistent for me.” Groth was out-aced by Mahut (10 to 7), but won 77 percent of his service points to 58 percent for the Frenchman. Mahut saved seven of nine break points. Groth will play second-seeded Ivo Karlovic in the semifinals. Karlovic won their only meeting 7-6 (4), 6-3 at Delray Beach in February.