Trailing the four-match series 2-0, the India bowlers restricted Australia to 259-5 on Boxing Day at the MCG.
Seamer Shami posted figures of 2-55, claiming the wickets of Chris Rogers (57) and Shaun Marsh (32), but he named Ashwin (1-60) as the key figure for India as they bid to salvage the series.
"It is great if one end is held tight, then you can attack from the other end," Shami said.
"Ashwin did that very well today and I was able to attack from the other end. We have to bowl as a unit. Ishant [Sharma, who posted 0-54 from 21 overs] was unlucky but he bowled really well.
"He has taken wickets earlier in the series so it's not like he isn't in form or is bowling badly. He is bowling well and we have to support each other as an attack.
"Throughout the series, our intention has been to bowl to a plan, to bowl line and length. But plans don't always work.
"Sometimes it isn't the bowlers' day, so line and length goes awry. Sometimes you don't get wickets or give away runs even when you bowl well. The focus today was on line and length, and I am glad that today we did that."
Shami missed the second Test at The Gabba through injury and left the ground during play on Friday due to another niggle before returning to bowl the final over of the day.
"I just strained my left thigh and went out to avoid any injury," Shami added. "I stretched and came back to bowl the last over.
"We will come out tomorrow to bowl Australia out early. If we can finish their innings in the morning session, then that will be good for us."