The win keeps the club fourth, increasing the gap to seventh-placed Newcastle to eight points with five regular-season games remaining.
However, they will be without Krishna for their next match after the Fijian striker was shown a second yellow card late in stoppage time.
The night was emotional in Wellington, with the teams and spectators observing a moment of reflection before kickoff following the Christchurch massacres on Friday.
The Phoenix quickly had the Wanderers under pressure and when a stray pass fell into Krishna's path, he scurried into the box and sneaked a shot past Wanderers keeper Vedran Janjetovic with next to no angle to work with.
After scoring his 15th goal of the season to become the Golden Boot frontrunner, Krishna pointed his hands to the sky before dropping to his knees in prayer as a tribute to Christchurch's terror attack victims.
Both teams enjoyed plenty of possession in opposition territory but the Phoenix looked more likely to score next. Midfielder Mandi stepped up in the 23rd minute, bending a free kick into the top corner.
When Williams scored 10 minutes later, the three-goal margin looked insurmountable for the visitors.
The Wanderers started the second half with purpose but weren't able to work a clear shot on goal until the 71st minute, when a free kick awarded on the edge of the area was upgraded to a penalty after a VAR review. But Alexander Baumjohann placed his spot kick wide of goal.
The visitors finally scored from an 86th-minute Mitchell Duke header but it was mere consolation as the Phoenix confirmed the points.
Wellington Phoenix 3 (Roy Krishna 12, Mandi 23, David Williams 33)
Western Sydney Wanderers 1 (Mitchell Duke 86)
Halftime: 3-1
