The Scots opened their preparations for next week's Twenty20 World Cup qualifiers with victory in their first-ever sudden-death eliminator. However, they had to come back from the dead after a woeful batting display saw them stumble to 109-8 in Nairobi.
Minnows Uganda were then firmly on course for a shock win when they needed just 19 runs from the final 30 deliveries with five wickets in hand.
The Saltires, who had been kept in the contest by spin twins Ross Lyons and Majid Haq, then staged a thrilling late fightback.
Richie Berrington led the way with two quick wickets and a brilliant run out. The Greenock star completed a thrilling all-round display when he held a catch off Ryan Watson's bowling from the final ball of the match with the scores level.
That forced a one-over eliminator during which Haq restricted the Ugandans to just five runs before Kyle Coetzer and Jan Stander sealed Scotland's win.
Steindl said: "We were cool under pressure when it really mattered but there is no doubt we got out of jail. We didn't put nearly enough runs on the board but we fought back well in the field.
"In fairness, we had six guys on the field who just arrived from Scotland on Saturday, so it was a big ask for them to acclimatise right away."
Batting first, the Saltires failed to dominate a dogged Ugandan attack with wickets falling at regular intervals. Stander top-scored with 25, including two boundaries and a six, while Nav Poonia and skipper Gavin Hamilton weighed-in with 20 and 17.
The Saltires step up their preparations today when they take on a Kenyan side who crushed the Ugandans by eight wickets on Saturday. Steindl added: "It was far too close for comfort and we know we will have to improve against Kenya."
Score summary: Scotland 109-8 (J Stander 25, N Poonia 20; S Ssenyondo 3-20); Uganda 109 (S Kyobe 51no; R Lyons 3-28, R Berrington 2-12, M Haq 2-21). Scotland won sudden death eliminator (Kenya 5-1, Scotland 10-0).
Pakistan coach Intikhab Alam has condemned stand-in captain Shahid Afridi's "unacceptable" actions after he was caught on television apparently biting the ball. Afridi is thought to be facing a two-match ban and was reportedly called into a hearing with match referee Ranjan Madugalle at the conclusion of Australia's two-wicket win in Perth, a result which completed a 5-0 one-day series whitewash.