The Ulstermen are on quite the run of late and are the only side with four wins from four in the European Cup while in the RaboDirect PRO12 they have won six of their last seven and currently sit fourth in the table.
"I am pleased to have signed for a further two years," said Best. "It is a massive honour to play for Ireland and Ulster. The support that I received when I missed out on the initial Lions squad was a massive factor in me making the decision to stay.
"That made me feel very special and underlined to me that Ulster is more than a team, it is a community and a rugby family. I want to keep playing for Ireland for as long as I can and to try and win a few more things in the green jersey."
Ulster are also boosted by the return to action of Paddy Wallace who takes the field for the province for the first time in nine months.
Wallace, who has made a record 188 appearances for Ulster, suffered an ACL injury against Glasgow in February. He returns to the senior team following two games for the Ulster Ravens in the British and Irish Cup.
He starts at inside centre and is one of nine personnel and three positional switches to the side that beat Treviso last weekend as head coach, Mark Anscombe, chooses to rotate his squad.
Ulster's only loss in their last 11 fixtures in all tournaments was a 17-9 defeat at the Scarlets in the RaboDirect PRO12 on November 2.
And the Ulstermen have lost just once at home since early February: 12-13 to Glasgow Warriors in round 2 of the RaboDirect PRO12.
The omens are not good for Zebre either - Ulster have met Italian opposition on 24 previous occasions in all competitions and lost only once: 12-23 at home to Treviso in October 2011.
Zebre meanwhile, are winless in their last ten contests in all tournaments since beating Cardiff Blues at the Arms Park in round 3 of the PRO12, although they did draw 16-16 with Scarlets in Parma on October 25.
The two sides have met on three previous occasions with Ulster victorious in each instance.
At Ravenhill Stadium , 7.05pm.
Referee: Neil Hennessy (WRU, 17th competition game)
Assistant Referees: Sean Gallagher, Dermot Blake (both IRFU)
Citing Commissioner: Wayne Sheridan (IRFU)
TMO: Simon McDowell (IRFU)
LIVE on BBC NI