user60422: I made a small box containing Arduino Pro Mini , DFPlayer Mini player and a 3.7V LiPo battery. Is it possible to power two devices with 3.7 V Battery? 
What is the best way to save power for longer time performance? 

user2967: Use a buck/boost voltage regulator. Those are high efficiency switching regulators, and can either increase or decrease the input voltage. Feed the output of the regulator directly into the Arudino's 5V (or 3.3V) line, bypassing the on-board voltage regulator.
What input voltages do the 2 devices need? Both 5V? If so, you can use a single voltage regulator to power both devices. If one needs 3.3V and the other needs 5V you may have to have 2 different voltage regulators.
By using a switching regulator you can bypass the fairly inefficient linear regulator in your Arduino supply 3.3V or 5V to it directly (depending on the type of board you have.)
Edit:
Ok, I looked it up and a DFPlayer Mini player appears to be a shield designed to plug directly into an Arduino. It looks like it can be powered from 3.2 to 5V, so you should be able to use it with either a 3.3V or 5V Arduino Pro Mini. Once you've decided if you're going to use a 3.3V or 5V Arduino, pick a buck/boost voltage regulator with the desired output voltage (or get an adjustable one and set it appropriately.)

60422: <p>I made a small box containing Arduino Pro Mini , DFPlayer Mini player and a 3.7V LiPo battery. Is it possible to power two devices with 3.7 V Battery? 
What is the best way to save power for longer time performance? </p>
 2967: <p>Use a buck/boost voltage regulator. Those are high efficiency switching regulators, and can either increase or decrease the input voltage. Feed the output of the regulator directly into the Arudino's 5V (or 3.3V) line, bypassing the on-board voltage regulator.</p>
<p>What input voltages do the 2 devices need? Both 5V? If so, you can use a single voltage regulator to power both devices. If one needs 3.3V and the other needs 5V you may have to have 2 different voltage regulators.</p>
<p>By using a switching regulator you can bypass the fairly inefficient linear regulator in your Arduino supply 3.3V or 5V to it directly (depending on the type of board you have.)</p>
<h2>Edit:</h2>
<p>Ok, I looked it up and a DFPlayer Mini player appears to be a shield designed to plug directly into an Arduino. It looks like it can be powered from 3.2 to 5V, so you should be able to use it with either a 3.3V or 5V Arduino Pro Mini. Once you've decided if you're going to use a 3.3V or 5V Arduino, pick a buck/boost voltage regulator with the desired output voltage (or get an adjustable one and set it appropriately.)</p>
