No. You'll need a new PSU.
The 20+4 pin power connector is for your motherboard, and needs to be connected to that.
You need to use both the 6 and 8 pin connector on the GPU, plus the 4/8 pin CPU power connector.
I'd suggest getting a decent 500W+ PSU - look for tier 1 or 2 on this list:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Xigmatek isn't usually considered good quality in the first place - I'd be surprised if it could output the labelled wattage.