The 2015 champions are out to reclaim the title in Qatar and were given an early test against a stubborn opponent and a raucous crowd at Ahmad bin Ali Stadium.
Australia dominated the Group B match, but struggled to find a way through India's determined defence until goalkeeper Gurpreet Singh Sandhu failed to claim a high cross from Martin Boyle five minutes after the break and Irvine pounced to fire home from close range.
Bos, a substitute, had only been on the field for a minute when he converted Riley McGree's low cross at the far post to double the lead in the 73rd.
"We can improve on everything and the boys know that," Australia coach Graham Arnold said. "We have our standards and I have high expectations of the players and their performances and those expectations and standards need to be met."
The match was the first in the history of the Asian Cup to be officiated by a female referee, with Japan's Yoshimi Yamashita in charge.
Australia are two points clear at the top of Group B thanks to a 0-0 draw between Uzbekistan and Syria.
Uzbekistan are hoping to be the main challenger to Australia, but they failed to make their pressure count at the Jassim bin Hamad Stadium.
Syria looked to have taken the lead in the second half through Ibrahim Hesar, only for the goal to be ruled offside.
In Saturday's early match, Tajikistan, making their Asian Cup debut, held China to a 0-0 draw in Group A.
Alisher Dzhalilov came close to putting Tajikistan ahead in the first half, while China's Liu Binbin had a shot cleared off the line after the break and Zhu Chenjie saw a goal ruled out by VAR.
Reigning champions Qatar top Group A after a 3-0 win over Lebanon on Friday.
Iraq's Aymen Hussein turned from hero to zero as, moments after putting Iraq ahead, he was sent off, having received a second yellow card for excessive celebrations at Khalifa International Stadium.
Down to 10 men, Iraq could not withstand Jordan's fightback and conceded twice in stoppage time to end their hopes of winning the competition for a second time.
Hussein struck in the 76th minute to spark wild celebrations, including him sitting cross-legged on the field and mimicking eating.
Iraq's joy soon turned to frustration, though, when referee Alireza Faghani booked Hussein for a second time.
It got worse for the 2007 champions when Yazan Al Arab levelled in the fifth minute of added time, with Nizar Al Rashdan going on to drill in a winner two minutes later.
Jordan advanced as one of the best third-placed teams and took the lead in the first minute of first-half stoppage time through Yazan Al Naimat.
Suad Natiq equalized for Iraq prior to Hussein's fifth goal of the tournament sparking the chaotic finale.
Jordan will play tournament debutants Tajikistan in the last eight.
In the day's other match, Akram Afif delivered again for Qatar as the hosts and defending champions overcame Palestine 2-1.
Afif has established himself as one of the stars of the tournament, and if he can keep up this form he may yet achieve his ambition of joining a European club.
The forward struck from the penalty spot in the 49th — his fourth goal of the Asian Cup — as Qatar came from behind at Al Bayt Stadium, with Hassan Al Haydos having cancelled out Oday Dabbagh's clinical finish.
Qatar will play either Uzbekistan or Thailand for a place in the last four.
Goals in each half from Mohamed Kanno and Faisal Al-Ghamdi at the Ahmad bin Ali Stadium in Al-Rayyan, Qatar, put the three-time champions in first place in Group F.
The Saudis have six points from two games and are two points ahead of Thailand, who earlier drew 0-0 with Oman. Third-place Oman have one point and Kyrgyzstan are pointless.
The task for Saudi Arabia was made much easier by Kyrgyzstan, who were making only their second appearance in the tournament, having a player sent off early in each half.
First to go was Aizar Akmatov for a rash challenge on Sami Al-Naji after just eight minutes.
Kanno broke the deadlock 10 minutes before the break, volleying home Saud Abdulhamid's cross at the far post.
Seven minutes into the second half, Kimi Merk was also shown a red for a dangerous tackle.
It resulted in almost constant pressure from Saudi Arabia and, with six minutes remaining, Al-Ghamdi’s long-range shot took a deflection and went through the hands of the otherwise impressive Erzhan Tokotaev in goal.
"It is difficult to play against Saudi Arabia with 11 players but with nine it is too difficult," Tajikistan captain Tamirlan Kozubaev said. "We did our best."
Earlier, Thailand moved closer to securing a spot in the knockout stage of the Asian Cup after drawing 0-0 with Oman on Sunday.
There was little attacking action of note at the Abdullah bin Khalifa Stadium in Doha with a close-range header from Elias Dolah of Thailand in the 15th minute almost crossing the line before it was cleared.
Oman, who lost their opening game against Saudi Arabia, struggled to break through the committed Thailand defence. Issam Al-Sabhi came closest with a shot that was saved late in the game.
"We are so happy to get one point and everybody worked hard for each other," Thailand defender Pansa Hemviboom said. "We communicated well as a team to get this result."
Oman, with just a point from their opening two games, need a win in their final group match against Kyrgyzstan to keep alive hopes of a place in the knockout stage.
The top two teams from each of the six groups advance, along with the four best runners-up.
The next Asian qualifiers for the World Cup in Qatar were due to be staged on the final week of this month but are now set to be called off.
A FIFA statement released on Thursday revealed that an update on the fixtures will follow "in the coming days" after consultation with AFC member associations.
The next batch of Asian Cup qualifiers were also slated for this month but are similarly in line to be postponed due to the virus, which originated in China, that has killed over 3,000 people.
"FIFA and the Asian Football Confederation (AFC) met at the Home of FIFA to discuss football activities in Asia." a FIFA statement read.
"For both FIFA and the AFC, the well-being and health of all individuals involved in football matches remains the highest priority, and as such, a formal proposal to postpone upcoming matches in the Asian FIFA World Cup 2022 and AFC Asian Cup 2023 qualifiers will now be shared with the relevant member associations.
"FIFA and the AFC will provide an update on these fixtures in the coming days following consultation with the AFC member associations.
"FIFA will continue to monitor the situation in relation to COVID-19 in cooperation with the World Health Organisation (WHO), the confederations and the member associations.
"Information on other international matches may be provided by the relevant confederation or member association."
Next year's tournament was due to be held in China but, owing to the Chinese government's strict Zero-COVID policy, it was confirmed earlier in 2022 that the competition would be held elsewhere.
Qatar, which is gearing up to host the World Cup in November and December, has now been selected to hold the tournament, which will take place between June 16 and July 16, 2023 and involve 24 teams.
It will mean the reigning Asian Cup champions have the chance to defend their title on home soil, with Qatar triumphing in the United Arab Emirates in 2019.
There has been controversy surrounding Qatar's hosting of this year's World Cup, with particular criticism of the nation's human rights record.
The World Cup kicks-off when Qatar face Ecuador on November 20 in Doha.
