Chasing a revised 209 from 46 overs they reached home with just over six overs to spare.
India openers Gambhir and Uthappa (55) laid the foundation for run-chase with 104-run stand in 20 overs.
Gambhir also shared 61-run partnership with Yuvraj Singh (38 off 28)) and remained unbeaten on 84, his fourth one-day half century.
Earlier Gavin Hamilton and Neil McCallum revived the Scots, after a shaky start, with a stand of 82 and former skipper Craig Wright chipped in with little cameo to steer their side to a useful 203 for 9.
Dravid intending to capitalise the conditions decided to bowl first but the seamers often struggled with their line, Ajit Agarkar and RP Singh sending down three wides each in an over.
It was Agarkar who drew the first blood for tourists, trapping Navdeep Poonia in the fifth over.
Fraser Watts made an unconvincing six from 28 balls before he edged RP Singh to give keeper Mahendra Dhoni a simple catch off the last ball of the eighth over.
Majid Haq struck the opening boundary with an elegant square drive in the ninth over, with Watson cutting to the fence in the next during an encouraging spell for the Scots.
There was a moment of controversy with the score on 49 for 2, Watson trying to hit over the top and mis-timing to mid-off where RP Singh took a diving catch.
The Scotland captain stood his ground and after some confusion the umpires decided to reinstate him.
His reprieve was not significant as he clipped to square-leg four balls later without adding to his score.
The next ball produced another wicket as Haq top-edged a pull but a rain delay of around 35 minutes, which curtailed the innings to 49 overs.
Off-spinner Ramesh Powar was introduced in the 24th over but his sixth delivery was despatched gloriously back over his head for six by McCallum.
The Scots were able to rotate the strike fairly easily against Powar and leg-spinner Piyush Chawla, who was unable to gain much purchase in the cold conditions.
McCallum, who had a moment of fortune when a top-edged sweep fell just beyond square-leg, was out trying to cut Chawla's straighter one, only to get a faint edge and Dhoni did the rest.
Wicket-keeper Colin Smith played one memorable reverse sweep for four during which he performed 'the splits' and toppled over, but was trapped by Chawla, who began to look more dangerous as his fingers gradually warmed up.
Another hefty downpour took the players off and reduced the innings by a further three overs.
Scotland's seasoned campaigner Wright struck two boundaries in Agarkar's eighth over but the seamer claimed his second wicket with a slower one that decieved Hamilton to disturb his wood work. Wright struck a towering six off Agarkar in the last over of Scots innings before being found short of crease trying to steal second run after tapping the ball to short third man.
Scotland opening ball attack applied the pressure, and with some alert fielding they restricted India to just 15 from the opening seven overs.
Uthappa, the right-hander from Bangalore, after a unusual vigil in early overs, began to find his touch and was particularly impressive with some powerfully struck straight drives and on-drives.
Uthappa carted Dewald Nel for a massive six that sailed high into the back row of the mid-wicket stand. But Wright continued his impressive display when he nipped one back to take Uthappa's inside edge to disturb his timber in the 21st over.
Having played a sheet anchor role to his agressive partner Uthappa, Gambhir completed fifty from 76 balls and started to play with more freedom.
Meanwhile Dinesh Karthik, one of India's heroes in their 1-0 Test series win against England, departed early. Karthik trying for an ambitious lofted on-drive was holed at mid-wicket off Haq.
Yuvraj was promoted above Dravid, played a couple of eye catching on drives. He lofted Wright into the marquee at long-on as he amassed 16 of the Wright's final over.
Jon Blain claiming the final wicket to fall when Yuvi was yorked after an entertaining 38.
That brought Dravid to the crease against the team he played for in 2003 and the captain nonchalantly flicked rank full toss from Nel off his pads for four to get off the mark, and repeated stroke off Blain to secure the winning runs.
Scotland 203 for 9 in 46 overs (Hamilton 44, McCallum 41, Wright 37, Watson 24; R P Singh 2 for 26, Munaf 2 for 36, Chawla 2 for 42, Agarkar 2 for 54) lost to India 212 for 3 in 39.5 overs (Gambhir 85, Uthappa 55, Yuvraj 38; Haq 1 for 32, Wright 1 for 46) by 7 wickets (D/L method).