Captain Harmanpreet Singh and Abhishek opened India's account in the first quarter. Harmanpreet then scored again in the second quarter to give India a 3-0 lead.
Pakistan responded through Hannan Shahid, who pulled one goal back. India quickly restored their three-goal advantage, with Abhishek scoring his second to make it 4-1.
Sufyan Khan reduced Pakistan's deficit to 4-2, with the second quarter producing four goals, two for each side.
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India extended their lead again in the third quarter when Hardik Singh converted a penalty stroke to make it 5-2.
Pakistan continued to push in the final quarter and Shahid scored his second goal of the match to make it 5-3. India held on through the remaining minutes to secure the win.
India bounce back after England defeat
India began their World Cup campaign with a 3-1 win over Wales before losing 2-4 to world No. 3 England. India conceded three goals in the second half of that match.
Pakistan, meanwhile, lost 1-4 to England before drawing 3-3 with Wales. The team therefore needed a strong result against India to keep its campaign on track.
India's latest win also continues their strong recent record against Pakistan. They defeated their neighbours 7-1 and 4-3 during the European leg of the Pro League earlier this year. Pakistan's last win over India came in the 2016 Champions Trophy.
Pakistan return after eight years
India and Pakistan came into the match with contrasting recent records. India have won medals at the last two Olympics, while four-time World Cup champions Pakistan were returning to the tournament after an eight-year absence.
Pakistan failed to qualify for the 2014 and 2023 editions and did not meet India at the 2018 World Cup.
The last World Cup meeting between the two sides came in Delhi in 2010, when India, led by Rajpal Singh, defeated Pakistan 4-1.
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Pakistan's current squad has limited World Cup experience, with only captain Mahmood and Ammad Butt having previously played at the tournament.
Their preparations had also been far from ideal. In their opening match against England, Pakistan's penalty-corner protection equipment was left in the dressing room. Against Wales, they missed several chances before settling for a 3-3 draw.
Despite the contrasting form of the two sides, the latest India-Pakistan clash once again lived up to the rivalry's reputation. India held their advantage when it mattered most to secure a 5-3 victory and progress to the next round.