Edinburgh kicked off the season by edging past Munster at Thomond Park but couldn't make it an Irish double when Connacht came to Murrayfield on Friday evening and made off with a 14-13 victory.
A tricky test lies in wait next - a trip to the Liberty Stadium - with Ospreys looking to make it three wins from three.
Victories over Benetton Treviso and Newport Gwent Dragons represent a positive start to the campaign and as they look to extend that winning run Wales flanker Justin Tipuric, who underwent surgery in May, could hand Steve Tandy's side a welcome boost.
"Tips may be involved this week," said the head coach. "He's come through the early part of training.
"We've got another contact session and two days off, so we'll see how he pulls up after that."
Connacht have raised a few eyebrows already this campaign, seeing off the Dragons before Friday's battling win in Edinburgh.
Next up is reigning GUINNESS PRO12 champions Leinster, who travel to the Sportsground on Friday night.
Leinster, wounded by defeat at Glasgow Warriors in round one, come into the game off the back of a thumping victory over Scarlets but Connacht prop Nathan White is eyeing an upset.
"I think we have got to get the mentality of going out there each week and implementing our own game," he said.
"They have won more trophies than we have had sunny days down here so it is just not thinking about that sort of stuff and just thinking about executing our sort of stuff."
Ulster and Glasgow both picked up wins last weekend, against Zebre and Cardiff Blues respectively, each racking up 33 points in the process.
That contributed to a second high-scoring week in the GUINNESS PRO12, taking the try tally after two weeks higher than ever before in the competition.
And hopefully we will see more of the same this weekend, when Ulster visit the Blues and Glasgow look to make it three from three against the Dragons.
Elsewhere, Munster welcome Zebre on Friday and Treviso travel to Scarlets in search of their first points of the campaign.
Follow us on Facebook, join the conversation on Twitter, sign up to our YouTube channel for extensive match highlights and sign up for our newsletter for regular updates on the GUINNESS PRO12
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland