The smallpox vaccine would be a candidate for most impactful invention of the 18th century (the first smallpox vaccination, named for the fact that it was derived from a cowpox blister -- vacca being Latin for cow -- was administered in 1796).
The form of the vaccine that allowed us to undertake global eradication was much newer:
"
In the late 1940s and early 1950s, Leslie Collier, an English microbiologist working at the Lister Institute of Preventive Medicine, developed a method for producing a heat-stable freeze-dried vaccine in powdered form.[50][51] Collier added 0.5% phenol to the vaccine to reduce the number of bacterial contaminants but the key stage was to add 5% peptone to the liquid vaccine before it was dispensed into ampoules. This protected the virus during the freeze drying process. After drying the ampoules were sealed under nitrogen. Like other vaccines, once reconstituted it became ineffective after 1–2 days at ambient temperatures. However, the dried vaccine was 100% effective when reconstituted after 6 months storage at 37 °C (99 °F) allowing it to be transported to, and stored in, remote tropical areas. Collier's method was increasingly used and, with minor modifications, became the standard for vaccine production adopted by the WHO Smallpox Eradication Unit when it initiated its global Smallpox Eradication Campaign in 1967
" -- https://en.wikipedia.org/wiki/Smallpox_vaccine
Yes but we're talking about the century in which the technology had an impact, not the century in which it was invented. The telephone is a 19th century invention which is only reaching the majority of the world's population in the 21st. Likewise the bicycle was a 19th century invention that really hit home in the 20th.
The smallpox vaccine is a strong contender. Smallpox killed 300m people in the 20th century, more than all wars combined. And we wiped it out.