The Reds were down, 2-0, until light-hitting catcher Chuckie Robinson clubbed a two-out, two-run homer in the seventh inning.
Cubs relief pitcher Brandon Hughes issued a four-pitch walk to Stuart Fairchild to open the ninth and Steer delivered.
The Reds have one more game, Wednesday afternoon against the Cubs, to prevent the 100-loss season.
What the win did was prevent the Reds from matching the club record 101 losses suffered by the 1982 team, the only Reds team to produce 100 losses in the long and historic franchise history.
But they still can lose 100.
The Cubs used a pair of solo home runs to take a 2-0 lead, a leadoff home run in the fourth by Willson Contreras and a leadoff home run in the seventh by Nico Hoerner.
As the midnight hour toward 100 losses approached, Chicago relief pitcher Keegan Thomspon struck out Steer and Michael Siani to open the seventh.
But he walked Jose Barrero and catcher Robinson drove a two-run game-tying home run into the right-field bleachers.
Reds starter Luis Cessa pitched 5 1/3 innings and gave up one hit and a walk but had to leave with one out in the sixth with a calf injury.
The one hit he gave up was hit by Contreras. Cessa struck out Contreras on three pitches, all fastballs, in the first. But his first pitch in the fourth was a slider and Contreras deposited into the left-field seats.
Hoerner’s home run was driven into the left field second deck off Fernando Cruz, who then struck out the side.
The Reds had two legitimate chances to score off Chicago starter Javier Assad.
They had two on with one out in the first on singles by Jake Fraley and Kyle Farmer, but Donovan Solano hit into a 6-4-3 double play.
They loaded the bases with one out in the sixth and didn’t score. Robinson singled, then Fraley and Farmer walked to fill ‘em up. Solano struck out and Fairchild popped out.
The Cubs put two on in the eighth with two outs against Buck Farmer, then Alexis Diaz came on to retire Ian Happ on a fly ball to shallow center field.
Diaz hit Franmil Reyes with a pitch with one out in the ninth, the 109th time a Reds pitcher has hit a batter, extending their major league record.
Pinch-runner Zach McKinstry stole second with one out, stole third with two outs and stayed there when Alfonso Rivas popped out, leaving it at 2-2.
Then came Steer’s dramatic hit to save the Reds from reaching the century mark in defeats.
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