Branko Radivojevic and Marian Gaborik, part of an all-Slovak line with Pavol Demitra, each had goals for the Wild, who are 5-0-1 all-time in home openers. Manny Fernandez made 29 saves for Minnesota, which spent plenty of money during the off-season to upgrade its roster.
The fans left delighted after Pierre-Marc Bouchard set up White with a drop pass that he deposited between Peter Budaj's legs to end it.
Richardson tied the game with 6:06 remaining in regulation on a long wrist shot from behind the right circle, using Petteri Nummelin as a screen. Colorado gained control after a Wild turnover, when Gaborik was hooked by John-Michael Liles without a penalty call and lost the puck.
The Avalanche, who lost at home Wednesday in overtime to Dallas after a strong start and fading down the stretch, looked like a team playing on back-to-back nights for the first period and part of the second.
Defence is not Colorado's strength, and Rob Blake leaving for Los Angeles sure didn't help. Neither does newcomer Jordan Leopold's hernia, which likely has him on the injured list for another month.
The Wild put plenty of early pressure on backup goalie Budaj (Jose Theodore started the opener), owning an 11-5 edge in shots in the first period and taking a 2-0 lead.
Gaborik signed a three-year, US$19 million contract shortly after his team traded a top prospect and a first-round draft pick to the Kings for his friend, Demitra.
It's a combination that could be devastating for opponents, provided they stay healthy. During the pre-game pomp, video of commissioner Gary Bettman's draft-day announcement of the Demitra deal was shown on the scoreboard - prompting a roar from the sellout crowd announced at 18,568.
Radivojevic, the defensive-minded member of this line, was the first to score off a rebound of Gaborik's shot. Radivojevic, who played his first five NHL seasons with Phoenix and then Philadelphia, whiffed on his first attempt but connected on the second and sent it to the back of the net.
Just 26 seconds into the middle period, Gaborik fielded a cross-ice pass from Demitra that sped along the red line and tapped it in for a 2-0 lead.
The Avs, who scored on two of their nine power plays against the Stars, woke up in the second half of the second period.
Richardson snagged a loose puck that got tangled in the linesman's skate near the boards and skidded past Minnesota's Kim Johnsson, another of the multimillionaires added in this summer's spree. Richardson had a clean breakaway, scoring off a swift move he made on Fernandez's glove side to cut the lead in half.
Colorado missed on many more prime scoring opportunities, especially on the power play, but Fernandez was sharp - helping stave off a five-on-three late in the second period - until Richardson's sudden rush following the turnover.
Notes: This was the first home opener Gaborik played in since 2002, due to a contract dispute, the lockout and a groin injury over the previous three years. ... Leopold was the Hobey Baker Award winner at the University of Minnesota.