It was Miami's first touchdown on a kickoff return since 1989, when Marc Logan scored at Houston at the end of a 39-7 blowout loss.
Welker's touchdown cut Baltimore's lead to 27-14, and the Dolphins got to within 27-21 when Sammy Morris broke loose for a 35-yard touchdown run on a third-and-2.
After Baltimore tacked on a field goal to make it 30-21, two dubious calls by the officials led to a Dolphins safety that gave us the final margin.
First, Travis Minor appeared to score on first-and-goal from the 1 when he reached the ball across the goal line after landing on a pile of bodies. In fact, one official signaled touchdown, but Minor was ruled down at the 1.
The officials ruled that the play had been blown dead, so no instant replay challenge was possible.
Two plays later, Rosenfels made a bad decision when faced with a pass rusher in his face and his bad pass was intercepted at the 2-yard line.
On the very next play, Jamal Lewis took a handoff and was stuffed at the 5. With Lewis still standing but his forward progress clearly stopped, David Bowens reached in and stripped the ball out.
It rolled in the end zone, was recovered by a Baltimore player for a safety when it seemed clear Lewis should have been ruled tackled at the 5.
Regardless, the Dolphins had one other serious threat the rest of the way, but Rosenfels took a bad sack (for a 14-yard loss) on a third-and-2 from the Ravens 28.
It was one of a few mistakes by Rosenfels, whose starting debuts was up-and-down.
He did throw for 264 yards, but was only 16-for-38 and was intercepted three times.
Things couldn't have started better for Rosenfels, whose first pass went for 76 yards and a touchdown to a streaking Chris Chambers as the Dolphins grabbed a quick 7-0 lead.
But Baltimore answered with 27 unanswered points, including a touchdown by defensive tackle Jarrett Johnson, who picked off an attempted screen pass at the 5 and rumbled into the end zone for the eighth score on an interception return against the Dolphins this season.
Another interception, returned 41 yards by safety Ed Reed, set up Jamal Lewis' touchdown run, which gave Baltimore its 27-7 lead early in the third quarter.
As they did every game under Jim Bates, the Dolphins battled to the end. But as they did too many times in this diastrous 2004 season, they came up short.