Encouraged by relative calm in the racially troubled Overtown area, Miami authorities went ahead with the Orange Bowl parade tonight in an effort to refocus attention on the city's sagging reputation as a carefree winter spa. The affair came off without a hitch.

The 49th annual pageant, with 33 floats and 25 marching bands, retained its traditional downtown route leading along Biscayne Bay and passing within three blocks of a perimeter sealed off by Miami police to contain violence that exploded Tuesday night over the police killing of a black youth in an Overtown video gallery. The Overtown area is just north of downtown.

Incidents on the rundown Overtown streets Thursday night and today were limited to occasional rock and bottle throwing at passing cars, police reported. As a result, the more than 300 policemen who had been stationed in and around the area began to go off duty, with the force dropping by about a third, a spokesman said.

Squad cars and orange-and-white barriers nevertheless remained along the perimeter a short distance from the parade's path. Their proximity symbolized the determination of Miami's leaders to have the festivities show the city in a good light after three days of negative publicity that officials complained could depress tourism receipts further. Despite the disturbances, the first parade spectators began waiting on the sidewalks at 5 a.m. today, and all 25,000 reserved seats were sold out in advance.

The police announced that they were stationing their "usual" 200 officers along the parade route, but scattered many plainclothes officers in the crowd to watch for troublemakers.

The burst of racial disturbance drew particular national attention because Miami has suffered two of the most violent outbreaks of urban unrest in the country since the mid-1970s. First came the Liberty City riots, in which 18 people were killed in May, 1980, and now the Overtown troubles, which police said have left two blacks dead and 26 blacks and white injured.

In addition, Miami has gained a reputation for violence--generally non-racial violence--over the past few years, largely due to its role as a cocaine and marijuana smuggling center.

But also contributing are lax gun laws and the sudden influx two years ago of 125,000 additional Cuban refugees. Many of them were common criminals who took up where they left off in Cuba after they reached here in a makeshift flotilla.

"It is no less true because we don't like it. The world thinks of Miami this week as the home of turmoil rather than as an international sports center," Miami Herald sports editor Edwin Pope wrote today in his preview of the New Year's Orange Bowl football game.

In some ways, the game is a measure of Miami's suffering tourism image.

Traditionally, the 74,224 Orange Bowl seats are sold out well in advance. This year, however, more than 2,000 have remained unsold, according to ticket officials.

Pope pointed out that lackluster sales were in part attributable to the relative importance of the game, which matches Nebraska against Louisiana State. More exciting, he acknowledged, were contests between Georgia and Penn State at the Sugar Bowl Saturday night and Sunday's professional game between the Miami Dolphins and the Baltimore Colts.

But the Overtown street violence reached within seven blocks due east of the Orange Bowl stadium. Mayor Maurice Ferre, in a gesture to dispel concern over the proximity, assured football fans that attendance at Saturday's game would be safe, and vowed to take his family to see it.

"I wouldn't expose my children if I thought there was going to be any danger," he announced.

The Metropolitan Dade County tourism director, Lew Price, nevertheless lamented the effect such street unrest is likely to have on Miami's tourist industry, saying it broke out "just when we were starting to see some light at the end of the tunnel."

This was a reference to a slight upswing in tourism earnings reported by Price's office last month after several years of decline, attributable in large part to the city's unsavory reputation. The agency had helped arrest the decline by coordinating a $1 million advertising campaign to lure visitors.

As another part of the campaign, Miami hosted a convention in October for the American Society of Travel Agents in a just-completed complex overlooking Biscayne Bay and across to Miami Beach.

In an effort to make the city look good for conventioneers, police rounded up nearly 400 people they said were drinking in public, fighting or loitering in the streets. After a judge intervened, however, 32 were released on grounds that Operation Clean Sweep had violated their constitutional rights.

At about the same time the city's leadership, in another show of sensitivity to the image problem, expressed outrage over a special report on Miami in a British magazine, The Economist. The Miami Chamber of Commerce canceled a luncheon that was to honor the author, Andrew Neil, and the Florida Department of Commerce pulled $35,000 worth of advertising that was to appear in the special supplement.

One section of Neil's article that most offended local business leaders said:

"Miami is not a good city in which to be black. Blacks, of course, have not fared well in any major American city. But their plight is particularly acute in Miami."

Ferre, in an interview with a Miami columnist today, expressed irritation at the city's seeming emphasis on its reputation rather than efforts at solving the ills that endanger it. After blaming the Reagan administration for cutting social programs designed to help areas such as Overtown, he conceded that other cities seem to be making more progress on race relations, and added:

"If this community gave it as much importance as we do the Orange Bowl parade and football game, then we could make major progress too. Is that too much to ask of people? I don't know. These are difficult times."