The fast-paced final saw Spain come home with the gold, while GB finished second after narrowly edging out Lithuania by 0.03 seconds.
"It's so fast and furious you just get your head down and go for it. When you pop your head up at the end you're like, 'what's happened?', and wait for the scoreboard to come up," Heath told the BBC after the race.
Hungary's Kozak paddles her way to a triple gold
"I could tell the Spanish were ahead of us but our race was on the other side of the course so I couldn't have guessed where we came."
Heath and Schofield won bronze in London 2012 after they were pipped to the line by Belarus, so had unfinished business for this final, which they had qualified fastest for.
"Liam has been killing me in training and I didn't want to let him down," Schofield added. "To get that is just amazing."
Brazil's Queiroz dos Santos secures third Olympic medal, misses out on gold
Great Britain's Liam Heath sprints to gold in the 200m kayak