Pakistan's senior batsman will miss the final Test against England to attend the funeral of his brother.
"Inzamam played two fantastic knocks and he was the difference between the two sides," said Vaughan.
Pakistan maintained their 1-0 lead in the three-match series after drawing the second Test against England on Thursday.
England snapped up three late wickets to leave Pakistan 183 for 6 at the close on the fourth day in the second Test, an overall lead of 199 runs.
Inzamam hit a record equalling 23rd century as Pakistan made 462 before reducing England to 113 for 3 at close on day 2 of the second Test.
Inzamam-ul-Haq equalled the record for the number of Test centuries by a Pakistani when he scored his 23rd hundred during the second Test against England.
Pakistan ended day one on 300 for four against England in the second Test
'It was a very important victory for us,' said the Multan-born Pakistan captain
England's pacemen took four wickets between them to restrict Pakistan to 244 for six at close on the first day of the first Test.
Pakistan captain Inzamam-ul-Haq fears that the outcome of the test series against England will be affected by a loss of overs due to fewer playing hours.
An Australian newspaper reported that Virender Sehwag and Inzamam-ul-Haq mocked at captain Graeme Smith during the Super Series Test.
Pakistan left out pace bowler Mohammad Amir from their 15-man Twenty20 international squad to face Australia.
Chairman Shaharyar Khan said the PCB has confidence in Inzamam's leadership skills and he would continue in the post for the rest of the year.
Pakistan skipper Inzamam-ul Haq has been given the vote of confidence by the PCB.
'I'm backing myself to show the lead to the other batsmen,' the Pakistan captain said.
Local mediapersons continue to blame Andy Atkinson for preparing a 'grassless' pitch at Multan despite the burly curator's clarification that it was Inzamam who had asked for the grass to be removed.
India's captain hurt his lower back while fielding in the fifth One-Day International against Pakistan in Lahore on Wednesday.
He injured his lower back when he dived to stop an off-drive by Pakistani captain Inzamam-ul Haq.\n\n
The Sri Lankan batsman will strengthen the Asia XI batting for the second Afro-Asia Cup ODI against Africa XI.
India has retained the same side that levelled the series 2-2. Pakistan has replace Afridi with Taufeeq Umar.
The Asia XI captain said his batsmen still "needed hard work in the nets over the next two days" to win the series.
Congratulate the left-hander on reaching the 10,000-run mark in ODIs.
Tendulkar, Ganguly, Azharuddin and Dravid appear in the list.
The selectors also named two newcomers in Rana Namid-ul Hasan and Ifthkar Rao, a tearaway young speedster.
Pakistan vice-captain Younis Khan believes Misbah-ul-Haq can fill the void in the team left by former skipper Inzamam-ul-Haq's retirement
Captain Inzamam-ul-Haq struck an unbeaten 64 to keep Pakistan in the hunt for a series levelling win against the West Indies on day three of the second and final Test.
They scored the 28 runs they needed for victory in four overs.
South Africa coach Mickey Arthur said he was proud of his players for forming a guard of honour for Pakistan's Inzamam-ul-Haq on Tuesday but expected them to stop him high-scoring on the third day of the second Test.
The Pakistan captain became the seventh player to appear in 300 one-day internationals.
Razzaq said that India skipper Virat Kohli and Pakistan's Babar Azam should not be compared to each other
The 35-year-old is hoping to accomplish what no other Pakistan captain has.
The dispute was sparked by selectors announcing a pool of players for this month's series without taking captain Inzamam-ul-Haq or Miandad into confidence.