Batting first, Prestwick set an impressive looking target of 253 for nine from their 50 overs.
But Uddingston eventually surpassed this with just two balls to spare by reaching 257 for eight in 49.4 overs.
There looked to be considerable doubt that Uddingston would achieve this target as they needed 14 runs from the final over to win.
But two late sixes from Ross Lyons helped the Lanarkshire side – who also owed a lot to the 100 runs scored by Anwar Hafeez – over the line.
The result means that Uddingston are at the summit of the table with five wins from their opening six league matches this season.
This gives the Tunnocks-sponsored side a whopping 89.34 winning percentage, ahead of second placed Prestwick who are on 85.60 per cent.
Delighted Uddingston captain Bryan Clarke told the Times and Speaker: “It was a really, really good effort from us.
“We had to get ourselves up off the floor after losing the week before and the guys were brilliant.
“Needing 14 runs from the final over was a great situation for Ross to be in.
“He is an attacking batsman so it almost helped him a bit.
“That is what he had to do. He had no option.
“And all that was set up by a brilliant hundred from Anwar, who is a really valuable player.
“If he peaks it gives us a great chance of winning matches.
“So we just need to build on that from here.
“There is no reason why we can’t stay up there challenging for the title this season. It is completely in our own hands.”
Uddingston will be trying to gain a swift bit of revenge this Saturday in a home league game against Clydesdale, who thrashed Uddy in a Scottish Cup tie just a few weeks ago.
“We were rotten in that game and they hammered us,” Bryan said. “We back ourselves to get back on track against them.”