David Legwand gave Nashville a two-goal lead in the first period. Colin Wilson scored early in the second and Sergei Kostitsyn made it 4-0 midway through the period to end Howard's night.
Howard got pulled after giving up four goals on 16 shots and was replaced by Joey MacDonald.
The Red Wings avoided getting shut out for the third time in four games late in the second when Ruslan Salei scored for the first time this season in his 53rd game with Detroit.
The Central Division-leading Red Wings had their cushion over second-place Nashville cut to five points.
Nashville had lost five of six with the lone win coming against Detroit 3-0 on Saturday night.
The Predators did have a setback in their victory in a quiet Joe Louis Arena, losing center Marcel Goc in the first period to an undisclosed upper body injury. He assisted on Nashville's first goal, giving him 24 points in 49 games this season.
Detroit has lost three of four, scoring four goals during the stretch.
Pavel Datsyuk's return on Monday in a 3-2 win over the New York Rangers helped the Red Wings - a goal, assist and three takeaways - but Tomas Holmstrom didn't make quite the same impact after missing nine games with a hand injury.
Holmstrom stood in front of the crease in his traditional position, but that didn't produce any redirected shots in the net or obstruct Rinne's view.
Howard had a clear view of Erat's goal, but couldn't get his glove on the wrist shot from the left circle a few minutes into the game.
The Predators scored their next three goals on rebounds.
Legwand knocked Dan Cleary off the puck in the right circle and scored from almost the same spot when Ryan Suter's shot caromed off Howard toward him.
Detroit had a chance to pull within a goal late in the first period and was denied by Rinne, who reached low to snatch Nicklas Lidstrom's slap shot.
Wilson scored about a minute into the second period and Kostitsyn had a goal 10:26 into the second, leading to Howard's departure. MacDonald made 14 saves over the last 1½ periods.
Notes: Detroit C Valtteri Filppula missed the game with an injured left knee and is expected to be out at least a week. ... The Predators are 19-0-2 when leading after two periods.