Finland's start to the championships could not have been better, as after a personal best of 51.65 set earlier this year, Baas got off to a good start in the outside lane in her heat, which allowed her to control the race from the front after the break, setting a new Finnish best of 51.42, clear of Emma Zapletalova of Slovakia.
The world number 44 was again on the outside when she returned for her semi-final in the evening session, but this time a slower start saw her immediately off the pace of Norway's Henriette Jaeger.
Jaeger continued to go hard, as Wadeline Venlogh of Haiti and Paula Sevilla of Spain failed to match her pace, while Baas found herself blocked off when trying to overtake the Spaniard on a bend, which knocked her off her rhythm and ended any hopes of a fast finish.
The Norwegian crossed the line in 50.95 to reach the final, while Baas came home in fourth in 52.36.
In the men's 60m, Riku Illukka narrowly missed out on qualification to the semi-finals, as he finished fifth in heat five in a time of 6.64, only two hundreths of a second behind Ali Al Bulashi of Oman, who finished second, behind Jamaica's Olympic 100m silver medallist, Kishane Thompson.
Illukka's time was equal to that of the slowest automatic qualifier, but sadly wasn't quick enough to be among one of the two non-automatic qualifiers.
In the evening session, Emilia Kangas threw 17.05m on her first attempt in the women's shot put final, but the former European under-23 bronze medallist failed to improve on that in her next two attempts, eliminating her from the competition at the halfway point, as she finished in 13th place.
The Finnish national champion was well over a metre off her personal best as the USA's Chase Jackson won her first world indoor title with a best of 20.14m.