The latter departed when edging a catch to wicket-keeper Prasanna Jayawardene off the bowling of Chaminda Vaas.
Chaminda Vaas took 4-33 in the South African innings, which saw Jacques Kallis top score with 74.
Once Tendulkar had departed with the total on 108, Vaas and his team-mates met with little resistance.
Vaas holds the Test record, although several other Sri Lankans run him close.
During the recent first Test against England, Sri Lanka included a W P U C J Vaas in their line-up.
The in-form Vaas did reach his second half century of the competition, before smashing Adil Rashid to mid-wicket on 53.
Yuvraj Singh scratched around for three off 21 balls before he was caught at mid-wicket off the bowling of Chaminda Vaas.
And he and Kallis made excellent progress after Herschelle Gibbs had fallen lbw to Vaas for nought in the fifth over.
Clay Smith lasted five deliveries before being trapped lbw by Vaas, and Lasith Malinga's slingy action accounted for Mukuddem three overs later.
Stand-in skipper Mahela Jayawardene was impressed by Sri Lanka's ability to win without several key players, including Marvan Atapattu and Chaminda Vaas.
You have Vaas, Buck, all these difference characters and the idea was that sometimes you do want to see a train wreck.
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Chaminda Vaas took 2-4 in a five-over burst with the new ball.
It would be fitting for a great batsman like Sanath Jayasuriya and fantastic bowlers like Vaas and Muralitharan to play in the final.
He was denied the chance of a five-wicket haul when Vaas yorked Tino Best for four, leaving Lawson unbeaten on the same score.
Zimbabwe recalled Craig Wishart to open with Grant Flower for this match but he was out for one, leg before to Chaminda Vaas.
Chasing 181 to win, Northants actually ought to have won after openers David Sales and Chaminda Vaas raced to 50 off just 27 balls.
Chaminda Vaas was Sri Lanka's star performer, taking 4-20 from 21 overs, and he now needs only two wickets to reach 300 in Tests.
The pair put on 53 before wicket-keeper Romesh Kaluwitharana took a low one-handed catch off the bowling of Chaminda Vaas to dismiss Boje for 31.
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After the morning session had been lost because of overnight rain Chaminda Vaas dismissed Narsingh Deonarine for seven and Dwayne Smith for a duck, both lbw.
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If we can repeat what happened 11 years ago it would be a great achievement and the crowning glory for outstanding cricketers like Sanath, Murali and Vaas.
But Dravid and Yuvraj put together an impressive partnership to give India hope, putting on 133 before Yuvraj was caught by Sangakkara off Chaminda Vaas for 46.
Marcus Trescothick quickly became frustrated, lofting Vaas to mid-on one ball after inside-edging an ambitious pull shot to the fine-leg fence, England's last boundary for 31 overs.
BBC: SPORT | Cricket | Sri v Eng | England humbled in Dambulla
Captain Mahela Jayawardene, Kumar Sangakkara, Chaminda Vaas, Muttiah Muralitharan, Dilhara Fernando, Sanath Jayasuriya and Upal Tharanga are among those to have signed lucrative three-year deals with IPL franchises.
Sri Lanka were without bowlers Chaminda Vaas and Nuwan Zoysa, but Lokuhettige picked up the mantle by bowling Mahendra Dhoni for two and dismissing Yuvraj Singh for 12.
If Andrew Flintoff had watched Strauss's dismissal he did not learn from it, the otherwise in-form all-rounder playing far too early to Vaas and holing out at short extra-cover.
BBC: SPORT | Cricket | Sri v Eng | England humbled in Dambulla
Captain Shivnarine Chanderpaul was lbw to Vaas in the third over of play without adding to his 69 and his dismissal ended a seventh wicket partnership of 81 with Banks.
Some observers have mentioned Vaas' quite amazing record against Kiwi skipper Stephen Fleming - he's dismissed him for a duck the last four times they have come up against each other.
The West Indies fast bowlers exploited the lively pitch and partly cloudy conditions early in the day but the complexion of the match changed again when Samaraweera was joined by Vaas.
West Indies managed to add only 14 runs to their first day score of 271-6 at the start of play as Vaas (3-35) and Lasith Malinga (4-71) mopped up the tail.
Left-arm seamer Chaminda Vaas gave the hosts a dream start when he removed opener Gautam Gambhir with the second delivery of the match, which moved in sharply to knock back the off-stump.
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