Captain Mirko Vučinić scored the winning goal as Montenegro edged past Moldova to maintain pole position in Group H.
Until Vučinić pounced at a corner 12 minutes from time, the hosts seemed quite comfortable. Ion Caras' team had given as good as they had got and looked good value for a point.
Moldova went close with numerous dangerous efforts in the first half, although they relied on keeper Serghei Paşcenco to keep visitors at bay on more than one occasion. Their hopes of earning a point were given a boost when, just after the hour mark, Montenegro midfielder Milorad Peković was dismissed for picking up a second yellow card.
Despite being a man down, however, Montenegro not only stifled their opponents going forward, they also clinched a winner through their captain. Marko Baša met Elsad Zverotić's corner, heading the ball to Vučinić, who beat Paşcenco from close range.
Moldova surged forward, trying in vain to steal a draw, but their overexuberence resulted in a red card for Alexandru Gaţcan, who collected two bookings inside a minute.
Montenegro play host to second-placed England on Tuesday with the chance to go five points clear in the section.