India, who last won an Olympic medal -- a gold -- at the 1980 Moscow Games, faced an aggressive Belgium side that scored thrice after conceding a goal against the run of play in the 15th minute.
Akashdeep Singh deflected from a close angle but Belgium hit back as Dockier equalised in the 34th minute.
Dockier gave Belgium the lead in the 45th minute and Tom Boon scored a field goal in the 50th minute to make it 3-1 -- the scoreline that remained till the end.
It was a game that saw Belgium pressed higher from the push-back, pappering Indian goalkeeper P.R. Sreejesh, who even though delivered a stunning show but it was not enough.
Both the teams went after each other aggressively and Belgium's quick and attacking play kept the Indians guarded.
However, the Belgian midfield, led by captain John-john Dohmen proved to be the difference and they kept marching ahead to the Indian circle.
In the 10th minute, Simon Gougnard crossed for Sebastian Dockier but the latter was met with tremendous challenge and could only half-heartedly contacted the ball before it was popped out of danger.
In the final minute of the first quarter, India took the surprising lead as V.R. Raghunath drilled a long ball 25 yards out straight at the Belgium goal through the middle and Akashdeep deflected the ball on the right post. The ball touched the left leg of goalkeeper Vincent Vanasch before entering the cage.
Belgium got a chance to pull level but Indian goalkeeper P.R. Sreejesh was all alert to block a deflection from Dohmen and latter Sreejesh again denied a penalty corner from Loick Lupayert as the first 30 minutes of play ended in India's favour.
However, Belgium hit back in the third and penultimate quarter and managed to score two goals through Dockier.
At the beginning of the second quarter, Sreejesh again came to India's rescue as he blocked a drive from forward Thomas Briels.
Belgium made barrage of attacks and in one of them, Sebastian Dockier scored a peach of a solo goal as he dodged past at least three defenders to push the ball past Sreejesh's outstretched right leg in the 34th minute.
As the match wore on Belgium looked more threatening and pappered Sreejesh from all angles. Penalty corner specialist Tom Boon tested Sreejesh but the Indian showed fine skills by diving to his right and deny Belgium the lead in the 44th minute.
But the European team took the lead one minute later when Cedric Charlier crossed from the left and Dockier dived forward superbly to deflect the ball in.
Belgum then further confirmed their strong position in the game when Boon scored a field goal from the top of the circle in the 50th minute.
Later, Belgium hardly gave anything away and quelled every Indian challenge to hold on to the scoreboard to enter the quarter-finals.
They will face either reigning world champions Australia or last edition's runners-up the Netherlands in the semi-final.
In the other last eight match, Argentina saw off a stiff competition from Spain with a 2-1 victory. Set-piece specialist Gonzalo Peillat gave the South Americans the lead in the 15th minute.
Spain equalised late through Pau Quemada in the 57th minute but Juan Gilardi sealed the win for Argentina with a field goal in the 59th minute.
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