Darren Cave and Robbie Diack had handed them the advantage in an error strewn game but with Mat Berquist slotting over four penalties, the Irish side were never truly comfortable.
But having held on for the 14-12 victory, they jumped up two places in the table to third with Treviso dropping down to 11th.
Reigning champions Leinster temporarily took over top spot before the weekend after powering to a 34-22 victory over Cardiff Blues on Thursday night.
Jack Conan marked his debut with a try inside three minutes before further scores from Richardt Strauss, Michael Bent and Eoin Reddan confirmed the bonus-point win.
The Blues enjoyed their best period either side of the break with Gareth Davies and Kristian Dacey both crossing but despite Dan Fish's second-half effort, they could not claw back the difference.
But it is Munster who sit top at the culmination of the weekend courtesy of a 25-11 win over Ospreys.
The Welsh side were flying high after demolishing Treviso 75-7 last time out but could only manage the one try this time through Ashley Beck.
Munster meanwhile saw James Downey score his first try for the club, with Sean Dougall and Simon Zebo also getting in on the try-scoring act.
While a thrilling encounter between Newport Gwent Dragons and Glasgow Warriors ended the way of the Welsh, who also saw 39-year-old Duncan Bell return to the game for his first professional match in two years.
The Warriors started the better, Rob Harley with a try after three minutes, but the hosts gradually worked their way back into the game with Ross Wardle's try ten minutes from time handing them the 24-23 win.
It proved a difficult weekend for both Scotland clubs as Edinburgh also slipped to defeat, this time 25-21 at the hands of Scarlets - Jordan Williams with two tries for the latter.
While Zebre remain rooted to the bottom of the table after a first-half blitz helped Connacht to a 27-19 win.
TRY OF THE WEEKEND
His charge down may have led to Ross Wardle's match winning try for Newport Gwent Dragons but Glasgow Warriors scrum-half Niko Matawalu had previously lit up the game with a fine solo run.
Latching on to a loose-ball, he ran the length of the opposition's half to get his side ahead just before the break.
The 80-metre run was one of the highlights of the day and one the Fijian would rather remember over his charge-down kick.
BREAK OF THE WEEKEND
They may have been on the losing side against Leinster but there were break aplenty from Cardiff Blues on Thursday, and one man at the centre of that was Dan Fish.
Fresh from signing a new contract earlier in the week, the full back capped his performance with a try but before that came a swooping break from inside his own half.
The move eventually led to Kristian Dacey forcing his way over before the break although they would be unable to bridge the gap to Leinster.
PLAY OF THE WEEKEND
Connacht powered themselves to victory over Zebre thanks in no small part to the power of their pack.
The writing was on the wall for Zebre as early as the fifth minute as a fine driving maul from a lineout saw Rodney Ah You dot down over the line.
And with a further penalty try awarded before the break, Connacht were already 22-0 to the good at the break to set them on the way to victory.
PLAYER OF THE WEEKEND
With George North leaving Scarlets over the summer, the stage was set for another man to step up to the mark.
And it appears Jordan Williams, who starred for Wales Under-20s at last year's Junior World Championships , is shaping up to do just that.
In his tenth appearance of the RaboDirect PRO12 season, Williams touched down for his third and fourth tries of the season, taking the man of the match plaudits in their 25-21 win over Edinburgh Rugby.
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