Katie Archibald (GBR) won silver and Justyna Kaczowska (POL) bronze.
On defeating four-time European champion Katie Archibald to win gold Brennauer said:
It's really great to win gold here. I know her quite well, she's my team-mate on the road (cycling) [they both compete for British professional cycling team Wiggle High5], and to beat her in front of her home crowd it makes me really speechless.
It was really great to race here in Glasgow with all these amazing people who came out here today.