Ottawa snapped a two-game losing streak. Detroit has lost two in a row.
Niklas Kronwall hit a post with a drive that could have tied the game just seconds later, but as the Red Wings pressed to get even, Clarke MacArthur scored into an empty net at 19:02 to give the Senators (6-3-2) the win.
"We didn't skate, and when you don't skate it's tough to win battles," Kronwall said. "We didn't even play in the first period."
Henrik Zetterberg scored the lone goal for the Red Wings (6-3-3), putting a backhander past Anderson at 3:34 of the third to make it 1-1.
"I liked the way we moved the puck out of our zone," MacArthur said. "We fumbled around with it a little in the second and the third, but I thought in the first we were direct, passes getting out and it makes it tough for them to forecheck.
"It was a great game. They have a great hockey team over there with a lot of speed, and every line there are guys that are dangerous. (Anderson) is a top-end goalie in this league and he showed it. For us to get that in regulation is a great feeling."
With the game tied 1-1, Anderson bailed out Karlsson with an acrobatic save against Tomas Jurco following a 2-on-1 rush that was created by Karlsson's giveaway at the Detroit blue-line.
Anderson was particularly busy through the final 40 minutes when he faced 30 shots. The Senators outshot the Red Wings 16-2 in the scoreless first period.
Howard was especially good during a nearly four-minute span in the second half of the period when the Red Wings took consecutive penalties.
The Senators had a 5-on-3 advantage for 20 seconds during that span but were unable to generate anything as they lost the initial faceoff after the second penalty, and the Red Wings iced the puck.
Kyle Turris beat Howard early in the second period but, by the time Turris took his shot, Howard was lying face down in the net, having been run into by a sliding Brendan Smith.
The goal was waved off as Howard was hurt on the play, however he stayed in the game and stopped Turris on a short-handed breakaway a few moments later.
"They really dictated the play," Howard said. "They really skated in the first period, and we didn't. It's tough to get the puck into the offensive zone when they're catching you from behind all the time.
"We did not do a good job getting the puck out at our blue line and getting it in at theirs."
The Senators got a puck past Howard that counted as Karlsson needed just 37 seconds of a power play to score on a shot from the point at 14:37. Turris earned the primary assist, his 99th in the NHL.
"The way this game went, it gives us momentum going forward even though this game was see-sawed," Senators coach Paul MacLean said. "I though the last eight minutes our leadership group did a really good job of settling things down, getting us the game and bringing this home.
"We deserved this."
NOTES: Colin Greening, Mark Borowiecki and Alex Chiasson were scratched for the Senators. Daniel Cleary, Kyle Quincy and Andrej Nestrasil sat out for the Red Wings. ... The Red Wings have won 18 of the 30 meetings between the teams. ... Senators general manager Bryan Murray was Detroit's head coach from 1990-93. Ottawa's current coach, Paul MacLean, was an assistant with Detroit from 2005-11.