If you haven't already, make sure your motherboard is running the last BIOS update put out by MSI.
For the motherboard, I'm going to suggest some things to troubleshoot. This effectively may affect how the system sleeps and what will wake it up. I'm going based on the manual on MSI's website, which describes the layout of the BIOS and (most) options therein.
Thers may be settings in the BIOS you can tweak relating to how the system sleeps (like if it only goes into S1 sleep, or S3 sleep) which you may want to read up on & fiddle around with, being sure to back up your current settings in case a change causes an issue. Looking at the manual, I would suggest checking...
> ACPI Settngs
> ACPI Standby State
(Switch the mode from S3 deep sleep to S1 normal sleep, or vice versa, depending on the current setting, and see if the screen wakes from sleep the way you want).
Also check, under
Settings > Advanced > Integrated Graphcs Configuraton
1) Initiate Graphc Adapter: if the system is set to check for an integrated graphics adapter before checking for a PCIe card, tell it to go for the PCIe graphics card first.
2) IGD Mult-Montor: (according to the manual, this allows integrated graphics to be used alongside dedicated graphics for Mult-Montor setups) ensure this is disabled, or set to PCIe graphics only.
ALSO check, under
... Advanced > Power Management
*EuP 2013: (according to the manual, when enabled, it is used "To reduce Power Consumpton when system off or standby mode") disable this, if possible
... Advanced > Wake Up Event Setup
1) Resume by PCI or PCIe device (disable)
2) (the similar options, wake by USB and wake by PS2 mouse/keyboard, can stay where they are, but you can try to disable them -- such that the power button on the computer is required to wake the computer)
I have no idea how things go if you just let the screen go to sleep automatically (rather than turning it off), but if that works (meaning you wake the computer and the screen wakes correctly with it), that may br the best workaround you have.