Baker praised her colleagues for acting so quickly but added, "The work of reform is far from finished."
Under current law, lawmakers must only disclose gifts with a value of more than $250.
Baker's bill, which now goes to the House for consideration, makes taking a cash gift below $250 a misdemeanor punishable by a fine of at least $1,000. A gift of $250 or more would be a felony, carrying the possibility of jail time.
A similar proposal has been introduced in the House, but it's unclear how quickly that chamber might act.
Last week, House leaders adopted a rule banning cash gifts - a rule the Senate has also adopted. That ban will be considered among several other ethics bills in the House, according to Steve Miskin, a spokesman for House Republicans.
Gov. Corbett has said he supports a cash gift ban.
The four lawmakers who took a total of $16,000 in cash from a wire-wearing lobbyist are House members. The lobbyist, Tyron B. Ali, had been secretly cooperating with state prosecutors.
Attorney General Kathleen G. Kane shut down the investigation, saying it was flawed and mishandled, though she has since said she believed there was evidence of a crime.
The House Ethics Committee is now reviewing the matter.
The Senate bill that passed Wednesday would ban any checks, money orders, debit cards, or gift cards to legislators. Exceptions would be a gift from a parent, spouse, child, or other close relative.
It excludes properly reported campaign contributions, commercial loans made during the ordinary course of business, gifts offered to the general public, and awards or prizes given out at a contest open to the public.
It also exempts "transactions of equal value" to cover lawmakers who buy and sell items or services either personally or in the course of operating a business.
Sen. Lloyd Smucker (R., Lancaster), a cosponsor of the bill, said ethics reform in the state legislature needs to be stronger.
"It is our responsibility to take direct and decisive action to change the culture, to strengthen ethical standards, and to make certain that enforcement follows infractions and that meaningful penalties are applied," Smucker said.
Smucker, chairman of the state government committee, has scheduled an April 28 hearing to address comprehensive change on all types of gifts and hospitality.
Sen. Anthony Hardy Williams (D., Phila.), speaking on the Senate floor, called the vote on the cash ban the beginning of an effort to reconnect with voters "who have had enough."
"This is a first step toward removing a stain cast on all of us," he said.