Paceman Avesh Khan got the first breakthrough for the home side, when he had Duckett caught by K L Rahul after the openers had added 82.
Holden went seven overs later, giving Jalaj Saxena, who plays for Kerala in domestic cricket, his first wicket in the second innings.
Hain and 21-year old Pope, a highly rated batsmen who has played two Tests so far, joined forces and defied the India 'A' bowlers for the next couple of hours.
They were willing to play the waiting game and didn't miss out on scoring opportunities.
The 105-run partnership went a long way in ensuring that the visiting team, who were at the receiving end in the ODI series preceding the 'Tests', stayed in the game.
The right-handed Pope played some attractive strokes as he picked up 10 fours in his 122-ball knock.
Hain was more restrained and his innings lasted 178 balls.
Pope became the first of Shahbaz Nadeem's victims, nicking one to 'keeper K S Bharat.
There was a brief stoppage due to mild showers and on resumption, the Lions lost two wickets before Steven Mullaney (3 from 38 balls) and Will Jacks (13 for 31 balls) knuckled down and denied India 'A'.
The match was called off when England Lions were ahead by 14 runs and teams decided a result was not possible.
India 'A' opener Priyank Panchal, who slammed a double century, was named man of the match.
The second unofficial Test begins in Mysuru on February 13.
Brief scores: England Lions 340 all out in 104.3 overs (Ben Duckett 80, Will Jacks 63, Sam Hain 61; Navdeep Saini 5/79) and 214 for 5 in 83 overs (Ollie Pope 63, Sam Hain 57, Jalaj Saxena 2/41) drew India 'A' 540 for 6 declared in 134.5 overs (Priyank Panchal 206, K S Bharat 142, K L Rahul 89; Zak Chappell 3/105). Man of the Match: P K Panchal.
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