Kilmallock and South Liberties have the only other 100% records after successive weekends of the championship.
After an eight-point win over Doon in round one, All-Ireland finalists Na Piarsaigh followed up with 16 points to spare over Ballybrown.
It finished 2-12 to 1-8 in Bruff after Na Piarsaigh led 0-12 to 0-4 at half-time.
The sides were evenly matched in the opening quarter but then four points from Alan Dempsey edged Na Piarsaigh clear.
Mid-way through the second half David Sheppard had the winners’ first goal to leave it 1-17 to 0-5.
Josh Adams had a late consolation goal for Ballybrown butt in injury time Adrian Breen cancelled that out with the second Na Piarsaigh goal. Shane Dowling ended with 12 points for the winners.
On Sunday evening in Newcastle West, Kilmallock produced a strong second half to see off Adare 2-17 to 0-14.
Adare dominated most of the first half but only led 0-10 to 1-6 at half-time. Kilmallock had a Gavin O’Mahony goal in the sixth minute when his free from distance ended up in the net and had his side 1-2 to 0-3 ahead by the end of the first quarter.
Willie Griffin and John Fitzgibbon scores ensured the interval lead for Adare.
Ger O’Loughlin’s Adare lost by 14 points in round one and were to score just four points in this second half as Kilmallock took over.
Six successive points moved the winners 1-14 to 0-11 clear as the game reached the final 15 minutes.
Graeme Mulcahy chipped in with five points from play and 10 minutes from the end Oisin O’Reilly had the second Kilmallock goal.
In Cappamore, a hat-trick of goals from William Hickey helped South Liberties to a 3-18 to 2-9 win over Knockainey.
The winners were 1-9 to 1-5 up at half-time. Brian Ryan had a return of eight points for the winners, while Knockainey free-taker Kieran Cleary had six points for the beaten side, who had two goals from Padraic Barron.
Patrickswell were the biggest winners in round one but they lost to Doon in Sunday’s round two game. It finished Doon 1-20, Patrickswell 1-17 in Kilmallock.
A Dean Coleman goal after eight minutes helped Doon to a 1-11 to 0-8 half-time lead.
Coleman and Pat Ryan had two points each for Doon in the opening half.
Early in the second half, Patrickswell began to battle back and a Josh Considine goal after 10 minutes helped reduce the gap to a single point entering the final quarter; 1-13 to 1-12.
Free taker Barry Murphy ended with 10 points for Doon and he had points in response to the Patrickswell rally, which included points from Aaron Gillane.
Inter-county man Darragh O’Donovan had two second-half points to maintain the Doon lead to the end.
Monaleen and Cappamore ended 1-13 each on Saturday in Kilmallock. Monaleen needed the last two points to ensure the lead.
Cappamore had led by nine points early in the second half. The east Limerick men were 0-10 to 0-5 up at half-time with frees from Tommy O’Donoghue and Bill Creamer points ensuring the advantage.
Creamer scored 1-1 early in the second half and Cappamore were 1-11 to 0-5 ahead. But they scored just twice more in the contest.
Monaleen had a John Nicholas goal 10 minutes into the second half to help kick-start their fight back and it was an injury-time Peter Russell free that levelled.
Murroe-Boher had a 0-13 to 0-12 win over Ahane with a 10-point return from Sean Tobin inspiring the newly promoted side, who suffered a one-point defeat in round one.
Tom Morrissey ended with nine points for Ahane, who finished with 13 men.
Both Tobin and Morrissey hit four points each from play.
At half-time Murroe-Boher were 0-6 to 0-4 ahead with Aaron Kennedy their only scorer outside of Tobin.
Dylan Sheehan and Mikey Ryan had second-half points for Murroe-Boher who were three points clear with the winning line in sight.
John Fox and Morrissey had late Ahane points but they couldn’t find the equaliser.