i5-4690k Overclock on H81 Mobo

Okay, so I have an MSI H81M-P33 motherboard. I didn't buy this motherboard with overclocking in mind, obviously. But I just recently upgraded from an i3-4160 to an i5-4690k because I found it so cheap, or else I would have gotten an i5-4590.

Anyways, I've tested its overclocking potential and I've reached 4.3GHz stable, but it crashes Windows at 4.4GHz after playing Battlefield 1 for only a few minutes. I was able to run Firestrike and Firestrike Ultra at 4.4GHz, but it crashes during BF1. Load temps are around 65-68C just before crash.

So to my question; is my H81 motherboard the limiting factor here? If I wanted to go higher would a better mobo allow this? Or are there some 4690k's that only get up to 4.3GHz stable?
 
Solution
The board is surely the limiting factor. It only has a 2+1 phase system (2 for CPU, 1 for memory) so it probably is unable to provide proper power at higher clocks.


$100 if I decided to upgrade. Give or take $10.
 


Well, the thing is what I have now is working well for me. Anything more would be simply for enjoyment. So, I might just wait til after Christmas to upgrade again as I just bought the i5 and a GTX 1060.

Thank you for all the help though. I really like those motherboards you picked out as well as the be quiet coolers. Cheers. :)