The report What Do Graduates Do? is based on analysing the careers of more than a quarter of a million UK graduates immediately after they leave university.
It suggests graduate employment is up from 64.9% in 2013 to 66.3% in 2014, with the number studying for a second degree or postgraduate qualification falling from 13% to 12.4%. The number of recent graduates going into 'non-professional' roles such as waiting and bar work has also decreased from 13.7% to 13%.
There has been a marked improvement in fortunes for graduates from STEM subjects. The number working in sciences has seen a year-on-year increase of 22.4%.
Engineering and building students saw some of the highest rates of employment across the board, with 83.6% of architecture graduates employed within six months and only 6.1% unemployed.
HESCU deputy director of research Charlie Ball called the figures a "fascinating example of how quickly the graduate market can change".
"The biggest turnaround has been the outcomes of graduates from STEM and construction-related subjects," he said. "It’s encouraging that STEM skills are so highly sought, but there is a complex story of demand and supply.
"So it’s vital that students seek careers advice early and undertake work experience to better inform their decisions and prepare for employment."