Goals from Antonio Cassano, Andrea Ranocchia and Diego Milito were enough to see off a Chievo side for whom Luca Rigoni had earlier cancelled out Cassano's opener.
Stramaccioni was handed a vote of confidence by president Massimo Moratti after the 3-1 defeat at Siena last weekend, with reports in Italy suggesting he had been given five games to turn Inter's fortunes around.
The Nerazzurri players certainly did their bit to aid the 37-year-old's cause by turning in an impressive performance on a night full of plusses for Stramaccioni, who also welcomed back Milito and veteran midfielder Dejan Stankovic from injury.
Inter scored in just the second minute when a partially-cleared corner went back to the original taker Cassano and his cross-shot was fumbled over the line by Chievo goalkeeper Christian Puggioni.
The Flying Donkeys responded well and, in the 12th minute, almost levelled when Francesco Acerbi sent a free-header wide with only Samir Handanovic to beat.
They did find an equaliser nine minutes later through Rigoni, who pulled away from his marker to head past Handanovic from the edge of the six-yard box.
Inter were stung into action and Esteban Cambiasso brought a fine save out of Puggioni.
But there was nothing the visiting goalkeeper could do after 26 minutes when Ranocchia rose highest at a corner to power a header into the net.
Inter were now in full flow and Walter Gargano almost added a third before the break with a shot which hit the post.
Milito, making his first appearance since January 12, did make it 3-1 within five minutes of the restart, taking a Cambiasso pass before turning to fire clinically into the left corner.
Chievo never looked like getting back into it and Puggioni prevented a heavier defeat with some smart stops.
The first, after 52 minutes, saw him smother Rodrigo Palacio's effort and then get up quickly to block the follow-up from Yuto Nagatomo.
Nagatomo was also frustrated by Puggioni with 12 minutes to go.
By then, Stankovic had made his first appearance of the season after undergoing Achilles tendon surgery in May 2012, replacing Cambiasso.