Andrei Vasilevskiy made flashy saves look easy and stole wins as the Lightning ran away with the Presidents’ Trophy.The goalie’s personal numbers weren’t on the same historic level, but they were more than enough to earn Vasilevskiy the Vezina Trophy as the league’s best goaltender at the NHL Awards show on Wednesday night in Las Vegas.His win wasn’t a given, but the 24-year-old made a clear case for the Vezina in his regular season, putting up career numbers. He was sixth in save percentage (.925) and ninth in goals-against average (2.40). Perhaps more important, he backstopped the league’s best team in its historic 62-win regular season, finishing first in the league with 39 wins.Vasilevskiy had high competition for the Vezina, including from former teammate and mentor Ben Bishop, now with the Stars, but finished with 90 percent of the first-place votes.In his acceptance speech, Vasilevskiy thanked his family, teammates, coaches and trainers, the Lightning fans and the organization “for the opportunity to play for the best hockey club in the world.”For his historic 128-point season, Nikita Kucherov won the Hart Trophy as league MVP, voted by the Professional Hockey Writers Association, and the Ted Lindsay Award, the MVP prize voted on by the players.“It’s a huge night for me and my family,” Kucherov said afterward. “But the main thing is Stanley Cup. We want to make sure we work harder than we thought we did (this season). All these individual (awards), it’s obviously nice, but the main thing is Stanley Cup for me.“When I came (to the United States), the main thing was just try and make the team. Now all my thoughts are just to win the Cup, and bring the Cup back to Tampa, because people deserve that. We’ve been playing good hockey, and I’m sure if we keep the team (together), we can bounce back.”The Lightning had two other award finalists: Victor Hedman for the Norris Trophy (best defenseman) and Jon Cooper for the Jack Adams Award (coach of the year).Hedman was surprised to be a finalist for the Norris, which was won by the Flames’ Mark Giordano. The Jack Adams went to the Islanders’ Barry Trotz, with Cooper coming in second.The Lightning’s Anthony Cirelli finished sixth in votes for the Calder Trophy (rookie of the year) and was 11th in voting for the Selke Trophy (best defensive forward), getting one first-place vote. Brayden Point was ninth on the Selke list, also with one vote for first place, and got a couple of votes for Lady Byng (most gentlemanly player). Ryan McDonagh finished eighth in the Norris results.Cirelli also made the NHL all-rookie team. Kucherov and Vasilevskiy made the All-Star first team and Hedman the second team.Tampa Bay took hits in the opening monologue from host Kenan Thompson, who gave the “folks from Tampa” a shout out and recognized the Lightning’s 62 regular-season wins and the record-tying zero playoff wins.“That’s what I like about them, win or lose, they set records,” he quipped.”The night’s best moments had nothing to do with the Lightning. Canadiens goalie Carey Price made an 11-year-old boy cry in the best way. The much-watched video of Price’s meeting with Anderson Whitehead, whose mother died of cancer this year, won the fan choice award for best fan moment of the season. Anderson, a big Price fan, was invited onstage in Las Vegas for recognition. He then was told Price had a video message for him, but the supposed video cut off and Price appeared onstage to surprise him. Anderson was crying as Price handed him a signed jersey with a lengthy personal message and invited him to next year’s All-Star Game. The best line of the night came from Islanders goalie Robin Lehner, in his acceptance speech for the Masterton Trophy (perseverance, sportsmanship and dedication to ice hockey): “I’m not afraid to say I’m mentally ill, but that doesn’t mean I’m mentally weak.”Lehner has dealt with alcohol and pill addiction but has been sober for more than a year while also receiving treatment for mental-health issues. Information from Times news services was used in this report.