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Petroleum can be separated by distillation because the hydrocarbons in petroleum are

(1) elements with identical boiling points

(2) elements with different boiling points

(3) compounds with identical boiling points

(4) compounds with different boiling points

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PhyCS

(4) compounds with different boiling points 
This is also called fractional distillation. This is one of the first things you learn when you learn chemistry or start organic chemistry.

Dejanras

Answer is: (4) compounds with different boiling points.

Gasoline consists of hydrocarbons with between four and twenty carbon atoms.

Gasoline is a mixture  of many different hydrocarbons: alkanes (paraffins), cycloalkanes  and alkenes (olefins).

Petroleum is mixture (solution) consist of several different hydrocarbons (alkanes, alkenes...).

This hydroalkanes can be separated from mixture (crude oil) using distilation (usually fractional distillation), because they have different boiling points.

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