The 28-year-old British paddler delivered a flawless performance, clocking a time of 98.94 seconds to secure her place on the podium.
After qualifying third-fastest in the semi-finals, Woods maintained her composure under pressure to claim her first Olympic medal.
A nail-biting finish saw Woods briefly climb to second place behind Australia's Jessica Fox - who clocked an impressive time of 96.08 - only to be overtaken by Poland's Klaudia Zwolinska.
In doing so, Woods emulated Helen Reeves as only the second British woman to make a K1 podium at an Olympics.
The final podium spot was then left hanging in the balance as reigning Olympic champion Ricarda Funk of Germany prepared to race.
In a dramatic turn of events, Funk incurred a 50-second penalty for missing a gate, handing the bronze medal to Woods.
