Emiliano Buendia scored the opening goal for Norwich after only four minutes, only for Craig Dawson to equalise six minutes later.
The win lifts Watford to four points above the relegation zone with four games remaining, while Norwich are one loss away from sealing relegation.
Speaking after the game, Pearson said: "It's not breathing space.
"We'd been unable to find a win so far and it's not been easy to acclimatise, but it's a very important win for us.
"We've now got four games in which we've got to pick up enough points to keep us up ourselves. We don't have an opportunity to not stay focused, it's really important."