The Australian played a full 90 minutes as substitute Philipp Zulechner scored in the 88th minute to rescue a 1-0 win over strugglers Ried.
Both teams were reduced to 10 men but Graz held out to inch a point clear of third-placed Rheindorf Altach, who lost 3-0 away to Rapid Wien.
Finishing second or third in the Austrian Bundesliga guarantees a passage into the Europa League qualifying rounds.
Austria Wien is currently three points off the pace in fourth, albeit with a game in hand.
Jeggo has quickly become a key figure in his first full season at the UPC-Arena, racking up 25 appearances as the three-time Austrian champions approach their best finish since winning the league in 2011.
The 25-year-old former Melbourne Victory and Adelaide United player returned to the country of his birth midway through last season and has a further two years remaining on his contract.