Mizunuma brace leaves Sven seeing double in AFC Champions League
Mizunuma's cheeky free kick routine put the hosts ahead just before half-time and he volleyed a stunning winner on 65 minutes, after Wu Lei had briefly put SIPG level.
The victory leaves FC Tokyo dreaming of their first Champions League quarter-final, while SIPG are up against it in next week's return leg in Shanghai.
Elsewhere, a brilliant Leonardo free kick earned 2006 champions Jeonbuk Hyundai Motors a 1-1 away draw against Melbourne Victory.
In Tokyo, Mizunuma opened the scoring on 43 minutes when he swept a close-range free kick low and through the legs of team-mate Sota Hirayama, who was standing in the SIPG wall.
Argentine playmaker Dario Conca was at the heart of SIPG's response and he set up the equaliser with a pass to Lu Wenjun, whose rebounded effort was snapped up by Wu Lei on 55 minutes.
But Mizunuma drilled Tokyo back in front 10 minutes later when he ran on to Yuhei Tokunaga's cross and volleyed side-footed through the arms of goalkeeper Yan Junling.
Shanghai SIPG are debutants this year but Eriksson's men have the look of seasoned campaigners, with Conca and Elkeson both winners of the competition with Guangzhou Evergrande.
Earlier, Melbourne went ahead through Besart Berisha's header in the fifth minute, only for Leonardo to equalise with his free-kick eight minutes later.
The Brazilian's effort went over the wall and into the top left corner, past the unmoving goalkeeper Lawrence Thomas, to give Jeonbuk the edge when they host the second leg.
It was an emotional night for veteran Victory striker Archie Thompson, who was given a standing ovation as he was substituted in his final home match after 261 appearances and 101 goals for the club.
"In the end I was disappointed we didn't win the game," said Victory coach Kevin Muscat. "I thought we limited them to very little chances and we had a couple of gilt-edged chances.
"Having said that, we are still in the tie, we have scored in every away tie this campaign and we look forward to next week."