Milwaukee (59-77) won two of three last week at Pittsburgh (79-57). The lone defeat came when Morton (6-3, 3.14 ERA) allowed one unearned run over 6 2-3 innings in a 7-1 victory Wednesday.
Morton had been 0-4 with a 6.25 ERA over his first seven starts against the Brewers.
"I think it's something people like to talk about because there's been some consistency in that regard but really what the team is doing really well is not thinking about yesterday or two weeks ago, it's the game today," Morton said. "If it's the Brewers, it's the Brewers, so be it. This is a different year anyway."
The right-hander improved to 3-0 with a 1.83 ERA in his last five starts.
He won't have to face Gorzelanny, who yielded four runs over 5 1-3 innings to cap a three-start stretch in which he surrendered 16 runs over 13 2-3 innings.
That convinced Milwaukee that Gorzelanny won't get a chance to compete for a rotation spot in 2014, and plan to use him exclusively out of the bullpen.
Manager Ron Roenicke instead is turning to Thornburg (1-0, 1.94), who has yielded two hits over 5 2-3 scoreless innings of relief against the Pirates this year. Thornburg will make his first start versus Pittsburgh.
The right-hander, who turns 25 later this month, has posted a 0.50 ERA in three starts this year, failing to receive a decision in any of them despite allowing only three runs - one earned - over 18 innings. Curiously, he went 0-9 with a 5.79 ERA in 15 starts for Triple-A Nashville.
"I try to tell people, relieving and starting are two such different things," Thornburg told the Brewers' official website. "They're both pitching, but they're completely different mindsets, different ways of pitching."
Pittsburgh starts a nine-game trip tied with St. Louis for the division lead. The Pirates won two of three at home against the Cardinals over the weekend, failing to seize a two-game edge in the Central with Sunday's 7-2 defeat.
Justin Morneau made his Pittsburgh debut Sunday, going 1 for 3 with a walk as he batted sixth in the lineup and played first base. The longtime Minnesota slugger was acquired Saturday.
"I'm excited by this opportunity, of doing something every day to help this team win, to do whatever it takes to get in the playoffs," he told the Pirates' official website.
Manager Clint Hurdle batted Neil Walker at leadoff Sunday for the first time. Walker went 1 for 4 to extend his hitting streak at home to 12 games, and now will try to improve on a .213 road average that is one of baseball's worst marks.
The Brewers began this six-game homestand by being swept in a three-game set by the Angels. Carlos Gomez, hitting .371 against Pittsburgh, had a two-run homer in Sunday's 5-3 loss.