Adam Marusic put the home side ahead at the Stadio Olimpico with a stunning strike 12 minutes into the second half.
Lazio had a penalty award withdrawn after a video review 10 minutes later and they continued to create most of the chances.
But Lithuanian midfielder Gineitis side-footed home the equaliser and lifted Torino (39 points) to 11th, and within one point of the top half of Serie A. Paolo Vanoli's men remain unbeaten since a Valentine's Day defeat at Bologna.
Lazio, meanwhile, moved above Fiorentina to seventh, equal with city rivals Roma on 52 points and four adrift of fourth-placed Bologna.
Earlier on Monday, relegation-threatened Parma gained a useful point in a goalless draw at fellow strugglers Verona.
Neither club were able to impose themselves in a game of few chances. Daniel Mosquera came closest for Verona when his early header came back off the post.
The draw at Stadio Marcantonio Bentegodi edged Parma slightly further from Empoli in the nearest of the three relegation places.
With eight games left Parma, who went winless in March and go to leaders Inter Milan at the weekend, are now three points above the drop zone.
Verona are two places and four points above, and still not out of danger themselves.
Cagliari, who sit between Parma and Verona, were the only one of the bottom nine teams to record a win this round.
