The Tottenham forward broke the deadlock with a close-range finish just after the hour mark at the Lusail Iconic Stadium.
Richarlison then sealed the points with a stunning acrobatic effort 17 minutes from time as Tite's side made a winning start in Group G.
The Selecao remain unbeaten in their opening match at the finals since 1934, when they lost 3-1 to Spain in the first round.
Unbeaten in their past 15 World Cup group games, Brazil controlled the first half, but without creating many goalscoring opportunities.
Casemiro tested Vanja Milinkovic-Savic with an ambitious effort from distance, while the Serbia goalkeeper was quickly off his line to prevent Vinicius Junior latching onto Thiago Silva's precise throughball.
The Selecao carved their opponents' defence open with a neat one-two between Raphinha and Lucas Paqueta in the 35th minute, but the Barcelona forward could only shoot straight at Milinkovic-Savic.
Brazil carried a greater threat after the break. Milinkovic-Savic rescued Serbia by denying Raphinha, who had dispossessed Nemanja Gudelj outside his own penalty area, while Neymar fired wide from close range.
Alex Sandro rattled the post from 30 yards before the Samba Boys finally broke through in the 62nd minute; Richarlison prodding home the rebound after Milinkovic-Savic parried Vinicius' initial effort.
Richarlison then gave Brazil breathing space in emphatic fashion 11 minutes later; controlling Vinicius' low, hard cross with his left foot, before swivelling and sending a magnificent acrobatic volley flying into the bottom corner with his right.
Tite's side almost increased their advantage as Casemiro hit the crossbar and Milinkovic-Savic denied Rodrygo, but the two-goal margin was enough to lift them to the Group G summit.