Martinez opened the scoring with a deflected first-half effort before Lukaku got in on the act with a stunning 63rd-minute solo goal in Tuesday's clash at Stadio Mario Rigamonti.
Milan Skriniar's own goal 14 minutes from time gave Brescia hope, yet they were left to rue missed chances by Mario Balotelli on what proved a frustrating outing for the striker against the side where he made his name.
Inter were deservedly ahead by the 23rd minute, although there was more than a slice of luck about their goal. Martinez's long-range effort took a wicked deflection off Andrea Cistana and looped over Brescia goalkeeper Enrico Alfonso.
GAMES, GOALS, EL TORO.— Inter (@Inter_en) October 29, 2019
ON FORM. pic.twitter.com/2DNpnDDMUr
Brescia were much improved in the second half, with Balotelli threatening with a low strike before failing to get a decisive touch from close range following a goalmouth scramble.
The home side were made to pay in the 63rd minute when Lukaku cut in superbly from the right and fired a fine left-footed shot from 20 yards inside the far post.
Balotelli had a header kept out by Samir Handanovic and blasted the rebound over, but Brescia pulled one back when the goalkeeper blocked Dimitri Bisoli's cross but saw it rebound in off Skriniar.
However, an equaliser in the closing stages proved beyond them and Inter held on to return to winning ways.
What does it mean? Inter back on track
Drawing 2-2 with Parma on Saturday was an opportunity missed for Inter, with Juve also slipping up in a 1-1 draw at Lecce.
Normal service was resumed in Brescia by Conte's men, who have won eight of their opening 10 Serie A games and have cranked up the heat on the Bianconeri.
Hungry Lukaku looks revived
Lukaku scored his seventh goal of the campaign - and what a strike it was. A powerful run down the channel before a clinical strike that left the goalkeeper with no chance - it was vintage Lukaku, who is thriving under Conte after a spell to forget with Manchester United.
Frustration continues for Balotelli
There were moments when the enigmatic ex-Manchester City and Liverpool striker demonstrated he can be a threat. Yet, when the chances came, the 29-year-old failed to take them and that has largely been the story of his season with just one goal to date.
Key Opta Facts
6 + 5 - #Inter have two players with 5+ goals scored in Serie A this season (Romelu Lukaku and Lautaro Martínez): the last campaign when they had two players with 5+ goals after 10MDs was back in 2012/13 (Diego Milito ed Antonio Cassano). Couple.#BresciaInter pic.twitter.com/dLyvSyw1sH— OptaPaolo (@OptaPaolo) October 29, 2019
- Conte is the first Inter coach to have seen his team score in all their first 13 games in all competitions.
- Martinez scored his first goal from outside the box in Serie A with his 11th in the competition.
- Roberto Gagliardini's assist for Lukaku was his fourth in Serie A and his first since April 2017 in a derby against AC Milan.
Inter travel to Bologna on Saturday, while Brescia are away to Hellas Verona the following day.