A fan with 3 holes for pins.

Solution
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Paperdoc

Polypheme
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Yes, it will work. The wrinkle you MAY need to adjust for is fan speed. A 3-pin fan connected to a 4-pin fan header that actually uses the PWM Mode to control its fans will always run full speed. You get good cooling, but no way to make the fan quieter if that full speed is not needed. However, many mobo fan headers CAN be changed in BIOS Setup to use the older Voltage Control Mode (aka DC Mode) so that they can control the speed of a 3-pin fan. SOME even do this automatically so you don't have to adjust.

When you get this hooked up and running, do this quick check to see whether you need to take any action. Open the case. Start up the system and watch that fan very carefully from the start. The normal sequence is that the fan will start up at full speed for a few seconds (up to 10), then slow down as the system gets a temperature measurement and decides that full speed is not needed. So if you fan does that, worry no more! But if it stays at full speed, then you may need to adjust.

You have not told us what mobo you have - maker and exact model number. SOME mobos actually can NOT make this adjustment. So, IF your fan always runs full speed, post back here the mobo details and we can advise exactly what you can do.