Reigning champions Juve dropped points for the third game running in Wednesday's 3-3 draw with Sassuolo and Inter took full advantage a little over 24 hours on.
Antonio Candreva opened the scoring with a first-half strike for the visitors, who rested Romelu Lukaku, Stefan de Vrij and a number of other first-team players.
Sanchez set up that goal, played a part in Cristiano Biraghi's drive the other side of half-time and then headed in a third for Antonio Conte's men, before Roberto Gagliardini rounded things off.
SPAL were nearly behind inside five minutes as Marcelo Brozovic's shot clipped the post.
The hosts held Milan to a draw here two weeks ago, though, and they gave Inter a scare when Andrea Petagna's deflected shot on the turn hit the crossbar.
But Conte's side edged in front eight minutes before half-time through Candreva's clinical finish past Karlo Letica after being played in by Sanchez.
The hosts were further dismayed three minutes later as a penalty shout for Samir Handanovic's challenge on Gabriel Strefezza was turned down following a VAR check.
Inter extended their lead nine minutes after the restart - Biraghi cutting inside and picking out the bottom corner with a good finish.
Sanchez was involved in that goal and Biraghi repaid the favour by swinging in a cross for the loanee to head in from five yards out with an hour played.
What does it mean? Inter's Scudetto dream still alive
Inter looked well out of the title race after taking one point from games against Bologna and Hellas Verona, but back-to-back wins in the space of three days has changed that.
Juventus have lost one and drawn two of their last three games and play fourth-placed Lazio next, offering Conte's men hope of further closing the gap with four games to go.
Sharp Sanchez steps up again
With Lukaku being given the day off it was left to Sanchez and Lautaro Martinez to lead the line.
Sanchez was lively throughout and now has a combined eight goals and assists since last month's restart - only Juve's Cristiano Ronaldo (nine) has been directly involved in more.
Handanovic let off
The usually reliable Handanovic endured a moment to forget in the comeback win over Torino and he was perhaps fortunate to avoid giving away a first-half penalty on Thursday.
The Slovenian goalkeeper made clear contact with Strefezza inside the box, but the SPAL winger was not going to get to the ball so the referee decided against pointing to the spot.
Key Opta Facts
- Inter haven't conceded a single shot on target in a Serie A away game for the first time since January 2017, against Palermo.
- Inter have hit the woodwork five times since the restart, only Roma have done so more (six).
- Candreva has scored three goals in his past five Serie A games, as many as he had in his previous 83 league outings.
- Sanchez has provided seven assists in a single league campaign for the first time since 2016-17, when he was playing for Arsenal in Premier League.
- SPAL have only collected 19 points in 33 Serie A games this term; none of the previous 18 teams with 19 or fewer points at this stage of the competition have avoided the relegation (in the three-points-for-a-win era).
Inter travel to fifth-placed Roma on Sunday and SPAL take on Brescia, the side directly above them in the table, on the same day.