Hawke's Bay finally declaring having scored 365/4, and Schaw and company showed their class with the ball as well.
The captain took four wickets in Wairarapa's first innings as his side bowled the hosts out for 127.
Schaw grabbed a fifth scalp in their second innings in which Wairarapa could only add another 105 runs.
Hawke's Bay will host Manawatū at Nelson Park in Napier in round four of the Furlong Cup next Saturday and Sunday.
Meanwhile on Friday night a pair of thrilling finishes in the premier club Twenty20 competitions could prove pivotal in determining the eventual winners of the men's and women's grades.
In round three of the men's Murray McKearney Memorial Cup Taradale just squeezed home for a win over Napier Tech at Taradale Park to remain undefeated.
Tech posted a total of 142/6 in the first innings, and Taradale needed every single on of their 120 balls to beat it.
Some tight bowling from Napier veterans Steven Smidt and Jesse Ryder had the hosts needing 37 runs from the final three overs to take the win.
While Tech continued to take wickets, Taradale were finding the boundary and they entered the last over with two wickets in hand, needing eight runs.
When Smidt trapped tailender Harry Cooper LBW it looked as though Tech would hold on, but Taradale managed a single off the final ball of the match to take the win. Brendan Quinn ended 35 off 14, including five fours and a six, to get Taradale home.
Napier Old Boys' Marist beat Cornwall by 32 runs at Cornwall Park with Bronson Meehan (82* off 59) and Matthew Sinclair (66* off 50) taking them to a first innings total of 161/1.
The hosts could only muster 129/8 in reply as they batted out their 20 overs.
Another grandstand finish in the women's premier grade saw Havelock North defeat the previously unbeaten Napier Tech and draw level with them overall after four rounds of the competition.
Aniela Apperley scored 47 runs off 42 balls to lead Havelock North to a first innings total of 124/2 at Anderson Park.
She also took the wickets of Tech openers Cate Pedersen (48) and Briar Cloake (caught and bowled for 53 with the second-to-last delivery of the game) to leave Tech one run short of their total.
Each team will have one more game against Taradale over the next fortnight to decide the overall title.