When a hydrocarbon such as petrol or paraffin wax are burned in excess of air in a laboratory, carbon dioxide and water are the only products. When petrol is burned in a car engine, nitrogen monoxide, NO, is also formed. Explain how NO is formed in an internal combustion engine but not formed when a small sample of petrol is burnt in an evaporating basin.

Hydrocarbons consist of entirely carbon and hydrogen. While the gasoline in a car engine is not entirely hydrocarbon, the majority of it is. In fact, the combustion reaction in your car does not involve nitrogen at all, and as such it can be deduced that the reaction itself is not producing the nitrogen monoxide. 
Instead, you need to look at the heat of the engine itself. Some gasses can react at high temperatures, such as those in the cylinders of an engine. Nitrogen monoxide is the product of one of these heat driven reactions. Inside the cylinders, more than gas and oxygen is reacting; gas is reacting with air. This air contains just about everything, and most of the time there is excess oxygen in the cylinder. To make nitrogen monoxide, free oxygen and nitrogen molecules react endothermically to produce nitrogen monoxide. 
Some nitrogen monoxide is released by burning fuel itself. Some additives contain nitrogen, so when fuel is burned nitrogen is released into the mixture, where it bonds with oxygen.
Other sources of nitrogen monoxide in nature are lightning strikes and places with exposed lava, such as volcanoes. 
The reason you don't see it in a lab setting is:
There are no additives in the fuel mixture.
The reaction is low temperature, and does not reach the activation energy for nitrogen to oxidize.
Most experiments will not look for additional products of a reaction not attributed to the reactants themselves.