Indeed, the window comparator is what you need. It requires two opamps. You don't need a "real" AND gate, however, if you use open collector comparators. In this case, you can wire the output of both comparators together.
The reference can be a simple resistor divider with three resistors appropriately sized, which gives both the 2.7V+0.25V and the 2.7V-0.25V. The references can be derived from a supply rail if you don't need it to be ultra high accuracy. Otherwise, you'll need a precision voltage reference (e.g. TL431).
Here is the circuit:
The input is V1, and the circuit to supply when the conditions are met is represented by Rload. It can be a led, a relay (don't forget the protection diode), anything...
Note: The supply rail I used is 5V (I assumed that were your supply), and I used LM393 (because I had this model at hand), but this is not actually a good combination. The common-mode range of LM393 is Vcc-2V, which makes it too close from your highest reference point. Use this chip only if your supply voltage is higher. Otherwise, use an IC with a larger common-mode input range (there are cheap dual rail-to-rail input comparators with open collector output available from many manufacturers).