Martinez fires Inter Milan past Atalanta in the rain
Inter are now five points clear of Juventus and six ahead of Milan after showing relentless spirit despite the conditions playing havoc with the run of the ball.
The away side suffered an early blow when French central defender Benjamin Pavard limped off in the first half.
Hakan Calhanoglu lifted their spirits with a confidently converted spot-kick on 40 minutes sending Inter into a welcome half-time break from the rain.
The fiesty Martinez ripped a curling shot round two defenders and into the top corner with an impressive effort on 57 minutes.
Inter lost 'keeper Andre Onana to Manchester United in the close season but replaced him with Swiss stopper Yann Sommer, who produced an assured performance with his saves, calls and mobility.
Former West Ham player Gianluca Scammaca was fortunate to see his pullback goal stand after a foul in the build-up, but at 2-1 it was game on again until Rafaele Toloi was given a straight red card late on.
After a tricky test, Inter can look forward to Wednesday's Champions League game at Salzburg, where a victory would send them through to the last 16.
Reigning Italian champions Napoli beat southern neighbours Salernitana 2-0 earlier on Saturday to climb provisionally into the top four.
Inter, Juventus and Milan are all still ahead of the champions, but Napoli appear to be putting early season jitters behind them as French coach Rudi Garci starts to make his mark.
This could have been a mismatch with bottom side Salernitana winless so far this season.
Napoli, who host Union Berlin in the Champions League in midweek, were without injured Nigerian forward Victor Osimhen.
In his absence Giacomo Raspadori slotted home on 13 minutes and Macedonian winger Eljif Elmas assured the win on 82 minutes with a curling shot after an impressive burst down the left.
The Arechi stadium, with a capacity of 37,000 and just 50 kilometres south of Naples, was two-thirds empty despite the derby and Filippo Inzaghi's side appear doomed to a long relegation scrap.