An underwhelming display from the hosts was rescued by strikes from Max Meyer and substitute Mesut Ozil, ensuring that Die Mannschaft are back to winning ways following their disappointing Euro 2016 exit earlier this summer.
Schweinsteiger found his range early on when picking out Meyer, who could only send a tame shot down the middle for Lukas Hradecky to collect with relative ease.
There was a big chance for new Arsenal defender Shkodran Mustafi to make the difference soon after, but he could only send his header over the bar when left completely unmarked inside the box.
It was far from a vintage first-half showing from the world champions, as they created just one real clear-cut opening which Mario Gotze failed to make the most of when rounding Hradecky and saw his shot blocked by Jukka Raitala in front of goal.
Germany did dominate things in terms of possession, though, and were unlucky not to edge ahead after Meyer slid the ball through for Kevin Volland, who was only denied an opener by Thomas Lam on the line.
Finland, still without a win since Hans Backe took charge seven games ago, were doing just about enough to keep their opponents out but did get another slice of fortune when Paulus Arajuuri's miscue came back off his own post.
Highly-rated centre-back Niklas Sule, fresh from competing at the Olympic Games in Brazil, did manage to get away another shot late in the half which was again dealt with comfortably enough by Hradecky.
There was a little worry early in the second half when Mustafi appeared to roll his ankle, forcing him to limp around the field, but boss Joachim Low decided against taking him off.
Finland were showing more attacking intent in the immediate stages after the restart, looking to get the ball into the box a little more, but they finally came unstuck 55 minutes in when Germany opted to take a more direct route to goal.
Gotze collected a ball over the top down the right and sent in a dangerous cross, which Volland stepped over to allow Meyer to sweep in 10 yards out for his first international goal.
Another big chance went begging for Gotze 70 minutes in when he saw a second shot blocked from close range, yet he soon recovered from that miss and slid in Ozil who soon helped seal the win for the hosts.
Ozil, who had only been on the pitch for 15 minutes or so, saw his shot-cross come back off the underside of Arajuuri's leg and into the far corner to put the icing on the cake - a goal that he will be sure to claim.
The night very much belonged to Schweinsteiger, though, who bowed out prior to that second goal when making way for Julian Weigl - ending an international career that has spanned 14 years and seen him pick up a total of 121 caps.