I don't have personal experience with 144hz, but here is another thread to reference.....
http://www.tomshardware.com/forum/id-2002237/gaming-monitor-hdmi-dvi-dealing-144hz-120hz-refresh-rates.html
HDMI versions up to 1.2 support the same data throughput as single link DVI-D.
A HDMI to DVI or DVI to HDMI adapter is converting to or from single link DVI-D, as the video signal for these two is identical and it is just the adapter that is required (HDMI can carry audio, but this is lost with an adapter).
This is sufficient for 1920x1080 (or 1080p) at 60Hz.
The monitor requires dual link DVI-D or display port for 120 Hz or 144 Hz.
These standards include support for higher resolutions and refresh rates.
Technically HDMI 1.3 or higher has the bandwidth required, but I'm not sure that refresh rates over 75 Hz are part of the HDMI standard.
HDMI 1.4 does support 4K signals at 30 Hz.
HDMI 2.0 supports 4K signals at 60 Hz, although this is very new and not yet implemented in any device I have seen.