With Barcelona having leapfrogged Zinedine Zidane's side to lead the way in LaLiga earlier in the day, Madrid needed a victory to move back to the top of the pile.
But Mallorca had other ideas and Lago stunned Madrid seven minutes by sending what was the home side's only shot on target in the entire match into the bottom-right corner.
Karim Benzema hit the crossbar before substitute Rodrygo Goes squandered a presentable chance and Madrid's hopes of a comeback were all but over when Alvaro Odriozola saw red in the 74th minute, with Mallorca holding firm to claim its first win over Los Blancos since 2009.
Madrid looked to have quickly settled into its rhythm but was behind when Lago skipped inside Odriozola and curled a superb finish beyond Thibaut Courtois.
Ante Budimir thought he doubled Mallorca's tally seven minutes later when he was set up by Lago, only for his fine strike to be disallowed for offside.
Benzema was inches away from restoring parity before the half-hour mark, his close-range half-volley bouncing back off the woodwork.
Vinicius Junior burst through Mallorca's ranks early in the second half and teed up Benzema, but the Frenchman sent his strike at Manolo Reina.
Rodrygo replaced Isco in the 66th minute and should have done better when he was fed by Benzema, his touch getting away from him and the opening evaporated.
But as the Madrid pressure was building, Odriozola received a second yellow card for a reckless lunge on Iddrisu Baba to round off a frustrating night for the visitors.
Reigning LaLiga champion Barca cruised to a 3-0 victory over Eibar to put the pressure back on Madrid.
Los Blancos failed to respond and now sit second, a point above this season's surprise package Granada and one behind Barca.
The rivals were scheduled to meet in El Clasico next weekend, but perhaps the postponement because of political tensions in Catalonia has worked in Madrid's favour.