Yeah, this is likely a problem with your motherboard when the CPU is at load. Budget AM3+ motherboards run 125W CPUs very poorly and they're never recommended as solutions and this one in particular doesn't even pretend to support 125W motherboards; it doesn't officially support anything above 95W.
That being said, I'd just underclock the CPU. I can't think of many reasons to tell you to sink this much money into playing games on a 2012 platform that's generally been a disppointment in gaming. Better off saving this money towards a Ryzen platform upgrade.
If you still decide to upgrade to a higher-end AM3+ motherboard -- and note that this is not my recommendation -- look for 990fx motherboards. It's hard to give an exact recommendation because these motherboards haven't been widely sold new at retail for years and you don't so much get to make a choice as to what motherboard to seek as much as choosing from what's out there and being sold at what prices at any given time.
If you do happen to run into a Gigabyte 970 UD3P board, that particular one does have an 8+2 power phase and that is usually the cheapester you'll find one with a reasonable VRM configuration. You'll have to check that for the individual motherboards you're thinking about purchasing.