The Senate Finance Committee yesterday unanimously approved Patricia Roberts Harris for the job of Secretary of Health, Education and Welfare in place of Joseph A. Califano Jr., who was fired by President Carter last week in a Cabinet shakeup.

As the committee was voting in its second-floor hearing room in the Dirksen Office Building, Harris was assuring members of the Senate Labor and Human Resources Committee, two floors above, that she does not expect to have nominees for high positions in her new department jammed down her throat by the White House staff.

In response to questions from Sen. Don Riegle (D-Mich.), who said he feared that the White House staff might be getting ready to "politicize" appointments and dictate who is to get top jobs in HEW, Harris said that in her two years as secretary of housing and urban development "it has not happened and I don't anticipate it happening" at HEW.

One of the reasons she has avoided conflicts, she said, is that "I make a habit of not surprising anybody" on cusses her recommendations carefully with the White House and does not leak them to the press or reveal them until there is mutual agreement in cases where it is called for.

Before the Senate Finance Committee voted, it heard brief testimony from David Stith, former director of housing management in the Greensboro, N.C., Office of HUD, accusing Harris of having "covered up" what he characterized as "massive corruption" in North Caroline HUD operations.

Stith claimed he had first revealed in 1975, two years before Harris became secretary of HUD, that government housing programs were being "ripped off" by local developers who were allowed to raise rents in U.S. aided projects and get higher rent subsides and the like without normal procedures and written approvals.

He said that when Harris became secretary in 1977, she sent investigators in and they "confirmed" his charges but instead of cleaning up the mess, she ordered him transferred to Denver. Instead, he took unpaid leave and continued to fight the case, he said, while making 86 applications for other HUD jobs. He told reporters later that he had been offered a HUD job here starting Sept. 10 and would take it.

However, a spokesman for Harris told reporters later that Stith's statements arose out of personnel disputes with his superiors and that the HUD inspector general and never received charges for documentation of fraud or misappropriation, only of procedural irregularities. The spokesman said the investigation to which Stith alluded had centered on personnel matters, not corruption, and that Stith's claim that Harris' investigation had "confirmed" corruption was incorrect.

Finance Committee Chairman Russell B. Long (D-La.), asked Stith to send documentary evidence and said he would order an investigation by the General Accounting Office. Sen. Bob Dole (R-Kan.), then moved that the committee approve Harris and it did. CAPTION: Picture, Harris with Sen. Harrinson Williams, head of Labor and Human Resources panel AP