But he picked up a tournament-ending hernia injury and was ruled out of the rest of the tournament in the Georgian capital, with Munster's David O'Callaghan called up in his place.
The 29-year-old Stevenson, who played 19 times for Ulster this past season, is expected to be out of action for six to eight weeks following the operation.
Meanwhile, Ulster Rugby are serving up some special present ideas in time for Father's Day this coming Sunday.
Ulster Rugby Season Ticket prices start at just £195 which will guarantee that your dad enjoys at least 15 action-packed games at Ravenhill including one pre-season friendly.
He will have priority booking for all Ulster away matches as well as Heineken Cup quarter-final, semi-final and final matches and also the RaboDirect PRO12 play-offs depending on qualification.
Your dad will also receive exclusive discounts from Ulster Rugby partners, including Hastings Hotels, Winemark, House of Fraser and many more.
Buy now online by clicking here (make sure you select the Father's Day pricing status and leave your own contact email address if your gift is a surprise).
Alternatively, you can call the ticket office on 02890 493222 (quoting Father's Day) before Friday to receive an exclusive printable, 'Ulster Rugby Dad's Season Ticket', to place inside your card.
Want to get the whole family involved? Then why not take advantage of Ulster Rugby's great family rates!
A Family Season Ticket can include a combination of 1 adult, 2 or 3 children, or 2 adults, 1 or 2 children, and includes 15% off each seated or standing ticket in the Memorial or Family area.
If you wish to stand pitchside, a Family Season Ticket entitles you to 10% off each ticket in the East and West Terrace.