After a goalless 90 minutes, the Argentine international's late strike saw the Old Lady extend their winning run to 10 matches to keep the pressure on at the Serie A summit.
The visitors created the first opportunity of the evening early on when Miralem Pjanic's free kick found Mario Mandzukic at the back post, but the striker could only direct his header over Thomas Strakosha's crossbar.
Juve had the ball in the net on the half-hour mark when Jordan Lukaku headed a corner kick beyond his own keeper, but a foul by Mandzukic during the build-up saw the goal correctly ruled out.
Heading into the match off the back of midweek cup fixtures, the two sides cancelled one another out in the second period, though Lazio felt they should have been awarded a penalty just after the hour when Lucas Leiva went down under Medhi Benatia's heavy challenge.
With mere seconds remaining, Dybala collected a pass from Daniele Rugani, beat two defenders and shot high into the roof of the net to break Lazio hearts and send the away supporters into a frenzy.
Juventus, who head to Wembley Stadium to take on Tottenham Hotspur in the Champions League next week, are just one point behind Napoli in Serie A following their latest win.
LAZIO (3-5-2): Strakosha; Felipe, De Vrij, Radu; Lulic (Murgia, 90'), Parolo, Leiva, Milinkovic-Savic, Lukaku; Alberto (Anderson, 70'), Immobile (Caicedo, 79')
JUVENTUS (3-5-2): Buffon; Barzagli, Benatia, Rugani; Lichtsteiner (Costa, 57'), Khedira, Pjanic, Matuidi, Asamoah; Dybala (Chiellini, 95'), Mandzukic (Sandro, 72')