The youngster scored in the first half to give the Premier League champions a deserved lead as Jose Mourinho used the game to give several academy and youth players match-time.
Chelsea should have won by more but Eden Hazard and Charly Musonda both sent chances wide.
Petr Cech started in goal and as captain in what could be his last game for Chelsea, with the veteran shot-stopper tipped to leave the club this summer.
Chelsea’s up-and-coming youngsters got a chance to shine in hot and humid conditions as the Blues survived a brief second-half scare to triumph 1-0.
The English Premier League champions were visiting the Thai capital for the first stop on a post-season tour that also includes Australia.
Youngsters Izzy Brown, Ola Aina, Nathan Ake and Solanke all began the match, with the latter showing why he was named Chelsea’s academy player of the year last week. There was also good work from Brown and Ake as they combined on the left wing.
Solanke, 17, hammered home a perfectly-executed volley in the 13th minute after a low cross from 18-year-old Aina received a light touch from Loic Remy before finding the scorer’s right foot.
Kiatisuk Senamuang’s All-Stars team, made up of Thai Premier League players, provided little resistance for the visitors.
But they nearly caused some embarrassment in the 67th minute when an on-target shot was cleared by a brilliant header from Chelsea defender Andreas Christensen.
Conditions for the visitors inside Thailand’s national Rajamangala Stadium were testing and both teams took regular water breaks.
The second half saw some of Chelsea’s more experienced players introduced, including captain John Terry, Cesar Azpilicueta and injury-prone Diego Costa, who was pulled off again after less than 20 minutes.
Hazard got a cheer from the crowd almost every time he went near the ball in the second half and the Belgium international had a couple of close shots.
The only yellow card of the evening went to the All-Stars’ Bangkok United defender Mika Chunuonsee after a fairly blatant handball halted what could have been a dangerous attacking run from Jeremy Boga.
Chelsea fly straight to Australia from Thailand as they face Sydney FC in another friendly on Tuesday.