At the Lee Valley Hockey Centre, India's domination earned them the lead through day's captain SV Sunil's 39th minute goal.
South Korea equalised through brisk counter in the 57th minute, only for Thimmaiah to reclaim the lead within 30 seconds with a fine deflection on Talwinder Singh's diagonal cross from left.
The narrow victory ensured India stayed in the hunt for a medal in the Champions Trophy. India now have seven points from four matches going into the last league fixture against World champions Australia on Thursday.
India's first foray into the Korean circle was in the 11th minute after Mandeep Singh snatched the ball from a defender on the right flank and sprinted into the circle.
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He wasted the opportunity by not squaring the ball to Talwinder Singh and instead tried to himself move up further, thereby narrowing the angle and feebly pushing straight into the goalkeeper's pads.
Two minutes later, the Korean striker Lee Nam-yong received a long aerial ball on deep in the Indian right wing, but was crowded out of possession by the defenders.
Defender VR Raghunath came to India's rescue with a good save in the 14th minute and also generated the Indian counter-attack, but the strikers were again at a loss of ideas after getting on top of the rival circle.
Chinglensana Singh opened up the Korean defence with a fine cross from the left flank in the 22nd minute, but Nikkin Thimmaiah faltered as the ball struck his foot.
Two minutes later, striker Sunil was not able to reach a long through pass from Akashdeep Singh into the vacant area before the Koreans mounting their first dangerous raid. The Indian goal had a close shave with goalkeeper PR Sreejesh blocking the flick from close range.
India's raids finally produced a goal in the 39th through Sunil, who exchanged passes with Akashdeep Singh and then side-stepped the onrushing goalkeeper to push the ball into an open goal.
(REOPENS FGN 41)
One-and-a-half minutes from the end of second quarter, Belgium had two chances to draw level -- first their captain John-John Dohmen was denied by Sreejesh and then 15 seconds from half time they wasted a penalty corner as India went into the breather with a one-goal cushion.
That was all India could manage in the match as thereafter it was all Belgium.
If not for Sreejesh India could have lost the match by a bigger margin as he came out of his line to again deny Dockier.
Belgium then secured their second penalty corner late in the third quarter but once again Sreejesh came to India's rescue to keep out Loick Luypaert's flick.
But 30 seconds from final break Belgium's relentless efforts bore fruit courtesy some sloppy defending by the Indians.
Trailing, India pressed hard in the final quarter but failed to create an open chance. The Belgian defence too was upto the task to thwart any danger to their goal.
Belgium earned their third penalty corner three minutes into the final quarter but Sreejesh once again made a great save.
Pressing hard for the equaliser, India left spaces in the their backline and Belgium pounced on the opportunity to extend their lead through Boon's strike.
India's campaign, thus ended in the Rio Olympics as there are no classification matches this time.
Earlier in the day, Argentina defeated Spain 2-1 to book their place in the semifinals.