Troy Deeney put Watford ahead but David Lopez pulled Brighton level from the penalty spot after Tommie Hoban was penalised for bringing down Kazenga LuaLua.
But two goals inside a two minute spell from striker Matej Vydra gave the Hornets a thoroughly-deserved victory.
Zola said: "Our target was to do better than last season (11th) and we need to maintain focus. We need to consolidate in this position.
"I didn't expect it to gel this quickly, which is good and positive. But the most important thing now is not to relax."
Zola heaped praise on two-goal striker Vydra, who is currently on loan from Udinese.
He added: "Matej has matured a lot. He has shown a lot of quality in front of the keeper and worked very hard for the team, and especially against Liam Bridcutt in the Brighton midfield."
Zola hopes to secure several of his players, currently on loan, on permanent deals and added: "Officially they are with us on loan but they want to stay. They are very committed to us.
"They may have joined us at the last minute but they are enjoying what they are doing."