The chamber voted 66-23 to approve the bill sponsored by Republican Rep. Curry Todd of Collierville, a retired police officer.
The measure abandons earlier efforts to impose an 11 p.m. to 5 a.m. curfew for carrying handguns where alcohol is served and to keep a total ban on establishments that enforce age-restricted entry.
House Democratic Caucus Chairman Mike Turner of Old Hickory told Todd he had been "a little mischievous" for supporting the time limits when the bill earlier passed in the House, but then quickly abandoned them in a negotiation session with the Senate.
"There's nothing mischievous about this," Todd responded. "I was never ever for the curfew."
Todd said he had only agreed to move the version with the time limits so he would have enough votes to move the measure through committees and to a House vote.
In March, Todd strenuously opposed efforts to strip the curfew from the bill and told reporters he wouldn't vote for a bill without the time limits in it.
But the Senate passed the proposal without the restrictions, and the House negotiating panel led by Todd agreed to that version last week. Todd told the chamber Thursday he considered the changes "minor."
Proponents of the curfew said they wanted handgun carry rights to extend to family restaurants that also happen to serve alcohol. The 11 p.m. curfew was meant to differentiate those restaurants from bars, since Tennessee law doesn't make an official distinction between the two.
State restaurant and police chiefs associations oppose allowing guns in bars, though Todd argued that law enforcement groups did not actively voice their concerns to him this year.
The Senate would have to agree with the House version before it can head for Gov. Phil Bredesen's consideration, but it appears likely to pass since the agreement largely reflects the measure originally approved on a 26-7 vote last month.
The Democratic governor has not said whether he would sign it into law.
The bill would take effect June 1. The measure would leave unchanged an existing ban on consuming alcohol while carrying a handgun, and restaurant owners would still be able to ban weapons from being carried in their establishments.