The Watsonians batsman, who won his first cap four years ago, finally came of age with 106 in a second innings total of 230.
That allowed the Scots to set their rivals a target of 342 for victory and, despite some resistance from Collins Obuya, the win was sealed with three overs of the third day remaining.
Chalmers, continuing on 79 not out, drove Hiren Varaiya through extra cover in the first over of the morning. His second scoring shot was also a boundary, pulling Nehemiah Odhiambo behind square. However, his progress to three figures became a much more fraught affair as cricket's infamous "nervous 90s" took over.
Chalmers had reached 91 when he shuffled forward and edged an Elijah Otieno delivery to first slip where a difficult chance went down. He looked to have settled with a lovely off-drive for 4 off the same bowler but, on 98, Chalmers had an let-off when Tanmay Mishra put down a slip catch off Varaiya.
The Watsonians batsman revealed his relief after finally notching his maiden century. He said: "It's a great feeling to get my first hundred for Scotland and to make an important contribution to the win. It got a bit scratchy as I got closer to the landmark and it was on my mind that I have got out in the 90s a few times in club cricket.
"Maybe I earned the bit of luck I got but the biggest emotion when I got there was sheer relief. It's a proud moment and great for me and Ali [Evans, who took six first-class wickets] as we went to the same school. This innings shows I can contribute at this level and it makes me feel I belong."
Evans and Chalmers were the stars of the show after coming in as two of the replacements for the county players who played in last week's one-day international wins over the Kenyans. Chalmers added: "I think it's great that when the county guys went back, other guys have been able to come in and keep the wins coming. Maybe that's what made Ali and me even more determined to do well and it shows that we have genuine competition for places."
Yesterday's haul gives the Scots maximum points and means they will go to Ireland for their final match with a chance of reaching the I-Cup final. Chalmers said: "We knew what we had to do and I think it was a great team effort. The game against Ireland will be another test but we will go into it with confidence."
Robin Brown, the Kenya coach, admitted more of his players needed to show the application of captain Obuya, who was left stranded on 91 as his side slid to a 152-run defeat.
"Collins has shown the way for us and it's just a pity no-one could hang around with him long enough. There is really no excuse for the way we batted at times, especially because the wicket played better than at any time in the match," he said.
"Over the series of games, I don't think we have had a single piece of luck but Scotland have outplayed us and showed more awareness. What we need to do is learn from this experience and take the positives.
"Our main aim is to be prepared for the Twenty20 World Cup qualifier later this year and then try to qualify for the 50-over World Cup next year," added Brown.