Genie Bouchard and Mason Rudolph could be getting serious ... the tennis star showed up to the Steelers game Sunday with friends to cheer on her new beau!!!

We broke the story ... Genie and the Steelers backup QB kicked off a romantic fling recently -- and clearly, the fire is still burning hot.

'Cause just weeks after 26-year-old Genie was spotted out and about near Rudolph's Pittsburgh-area home ... she headed to 25-year-old Mason's game against the Titans in Tennessee.