Chiasson scored his sixth goal in just his sixth career NHL contest since being recalled from AHL Texas on April 2 and the Stars improved to 45 points, pulling even with Detroit and Columbus for the Western Conference's eighth and final playoff spot.
"Of course, this is incredible," Chiasson said. "I try not to pay attention to the stats, I just concentrate on my game. This is great for us. We're right there right now, right in eighth place. The only thing that matters are the guys that believe in here."
Bachman has been outstanding since stepping in for the injured Kari Lehtonen early in the Stars' 5-1 win over Los Angeles on Tuesday, stopping 79 of 82 shots and winning all three contests.
Lehtonen remains day to day with a strained groin.
"I thought he made some solid saves, he cleaned up a lot of the stuff in front of him," Dallas coach Glen Gulutzan said. "I thought our D did a good job of keeping guys away from him and I thought our forwards did a good job of collapsing. But he was real solid for us."
Brent Burns scored for the Sharks, who were coming off a 3-2 shootout win in Detroit on Thursday and are 8-2-1 in their last 11 contests.
"We can't get too high, we can't get too low," San Jose coach Todd McLellan said. "We've got to play every minute of all 60 as hard as we can. I thought that was probably our downfall tonight. We probably gave away 13 or 14 minutes of valuable time and it cost us."
Antti Niemi, starting his 19th straight game, made 17 saves.
The Stars have outscored opponents 19-9 during their winning streak, not including the shootout goal they were awarded when they rebounded from a 4-2 third-period deficit to defeat the Sharks 5-4 in San Jose last Sunday.
"I really think we're starting to carve out an identity and figure out why we're successful," said Nystrom, who has three goals and an assist in the last five games after notching just two goals and an assist in the previous 22 contests. "There's a certain way we have to play. We're not a high-risk team. When we tried that earlier in the year, we just got picked apart.
"Now we're playing a more straight-line game, we're getting pucks in, we're getting bodies to the net, we're paying the price and that's what it takes to win."
San Jose controlled the action for most of the third period, outshooting the Stars 13-5, but they were only able to get one past Bachman.
"Our work ethic was there. We had the chances," said Sharks leading scorer Joe Thornton. "It was just one of those nights where you probably should have gotten the two (points) but just didn't."
San Jose pulled within 2-1 on Burns' power play goal at 5:56 of the final period. Bachman stopped T.J. Galiardi's shot from the edge of the crease, but the rebound spit out front, ricocheted off the skate of Stars winger Loui Eriksson and right to Burns, who swiped a backhander past Bachman's glove.
Bachman made several key saves to preserve the Stars' lead as the period went on, including a huge pad stop on Patrick Marleau's one-timer from in front, off a pass from Martin Havlat behind the net at 12:42.
The Sharks swarmed the Dallas zone after pulling Niemi in the final 1:28, but were unable to get most of their shot attempts through, as multiple Stars dropped to the ice to block shots. Bachman did get the knob of his stick on Marleau's blast from the high slot with just 4 seconds remaining to secure the win.
"That wasn't even anything compared to guys that are sliding, taking one-timers in the shin pads and stuff," Bachman said of his final save. "It's great, it shows how committed the guys are and how determined they are to get two points right now. It's great to see."
Dallas jumped out quickly, taking the lead just 1:57 into the opening period on Nystrom's seventh goal of the year. After receiving a quick pass from Trevor Daley at the Dallas blue line, Nystrom led a 2-on-1 rush into San Jose territory, firing a wrist shot from the left circle that beat Niemi inside the right post.
"I had a guy joining me late, (Erik Cole), and I looked and the D just stepped up and gave me the opportunity to walk right in and I shot it as hard as I could," Nystrom said.
Chiasson continued his recent run of success at 7:00 with his sixth goal in the last five outings. Just 22 seconds into a Dallas power play, Ray Whitney drilled a one-timer from the right point that Chiasson deflected from the slot past Niemi's blocker, just inside the left post.
"It was a smart play by Whits," Gulutzan said of the goal. "Our power play got us an important one, especially early. If you can get one on the power play, it helps, so (Chiasson) did a good job again."
The Stars were just 1 for 20 on the man-advantage over the previous six contests.
"Right behind the eight ball 2 minutes in isn't a good thing and three, 4 minutes later it's 2-0 and to play with a lead with the schedule that we're all playing at this time of year is real important," McLellan said. "Obviously, coming back from two, we weren't capable of doing it tonight."
The Sharks nearly broke through on their own man-advantage in the second period, but Bachman made three fantastic saves within 9 seconds. First, he denied Thornton's wrist shot from the high slot. Then at 11:41, he robbed Joe Pavelski on a wrister from in front, before managing to smother Marleau's rebound attempt.
After going 1-11-2 on the second half of back-to-back sets last season and beginning this year 0-4-0, the Stars have won three of their last four in that situation. ... With an assist on Nystrom's goal, Dallas C Vernon Fiddler extended his career-long scoring streak to six games, during which he's totaled two goals and 10 points. ... The Stars honored former D Derian Hatcher as part of their 20th anniversary all-time team. Hatcher, who played his first two seasons in Minnesota before the North Stars relocated to Dallas in 1993, skated for the Stars through 2003, helping them win the 1999 Stanley Cup. He was the first American to serve as captain of a Cup-winning team.