The fourth-innings chase is often regarded as the ultimate challenge for a batter. Let us see who have done the best in successful chases.
Most runs: (400+):

GC Smith is the clear leader here. He also has the most centuries (4) and most 50+ scores (10, followed by contemporaries Hayden, Ponting and JL Langer with 7). Also note CG Greenidge’s 214*.
Tendulkar, Dravid and Sehwag have the most runs for India.
Williamson and Karunaratne are the only current players here, with Amla, Cook and Younis from recent years.
Bradman is not here (but when he batted, a fourth innings chase was often not needed by Australia).
Highest scores in these cases (115 and above):
A total of 76 centuries have been scored here.

Only two double centuries, with KR Mayers scoring his on debut. The next highest in recent years was 153* by K Perera in 2019. There are Morris and Bradman in the same Test at Leeds in 1948, which was the only successful 400+ chase until India followed in 1976. (Years later, MA Butcher emulated Bradman’s 173* at Leeds).
The highest from India are not in the above list.
Viswanath (112) and Gavaskar (102) made their centuries in the same match in 1976, while Tendulkar and Laxman have made 103*.
Highest averages (Minimum 15 innings):

These 21 entries are the only ones with 15 or more innings. GC Smith leads here as well, with Ponting close behind.
From the recent past there are Cook and Amla. Tendulkar, Dravid and Sehwag represent India.
Kisrsten and Dravid are among those who did not score a century, although Hutton has a 98*.
We will take up bowling in 4th-innings wins in the next part.