Four points behind Lazio and Roma prior to Sunday's clash at Dacia Arena, Luciano Spalletti's side wasted no time in stamping their authority on proceedings - Mauro Icardi's 99th Serie A goal for the club putting them 3-0 up at the interval.
Icardi's effort in first-half stoppage time came just three minutes after Rafinha had doubled Inter's lead, Andrea Ranocchia having headed the visitors in front early on.
Udinese had managed to forge some opportunities prior to Inter's quickfire double, but both Valon Behrami and Kevin Lasagna failed to take advantage of some sloppy Inter defending.
Inter were on the wrong side of a VAR red card decision in their 3-2 defeat to Juventus last time out, but were helped by the system this time - Seko Fofana seeing red following a review.
Borja Valero added a fourth goal in the 71st minute and victory sets Inter up for a crucial clash with Sassuolo next time out, before they face Lazio in what could be a winner-takes-all encounter on the final day.
Superb defending from Danilo denied Inter the perfect start - the Brazilian brilliantly clearing Ivan Perisic's powerful header off the line.
Inter would not be kept out for much longer, though, as Ranocchia lost his marker to head home from Marcelo Brozovic's inswinging corner 12 minutes in.
2 - Andrea Ranocchia has scored two goals with his two last shots in Serie A. Minimal. #UdineseInter— OptaPaolo (@OptaPaolo) May 6, 2018
Spalletti's side would have been two up five minutes later if not for another goal-line clearance from Danilo, with goalkeeper Albano Bizzarri having rushed off his line to challenge Icardi.
Antonio Candreva should have doubled Inter's lead just after the half hour, but the former Lazio man - still chasing his first Inter goal of the season - sliced over from close range.
Udinese could have made Inter pay moments later, only for Behrami to head over from close range before Samir Handanovic pulled off a superb stop to deny Kevin Lasagna.
Those misses proved costly on 43 minutes, Rafinha regaining possession deep in Udinese's half before charging clear of the hosts' defence and slotting a precise finish into the bottom-left corner.
There was still time before the break for Icardi to make it 3-0, Bizzarri unable to keep out the Argentine's stinging drive at his near post.
4 - Mauro Icardi has scored in each of his last four games played in Serie A for the second time (the first in September 2016). Maurito. #UdineseInter— OptaPaolo (@OptaPaolo) May 6, 2018
Lasagna went close from distance as Udinese looked to haul themselves back into the contest after the restart, but any hopes of a comeback were effectively ended when Fofana received his marching orders.
Having initially awarded a free-kick for Fofana's late challenge on Perisic, referee Paolo Mazzoleni utilised the VAR system and decided the Udinese man had intentionally stamped on Inter's winger.
Matters were made worse for Udinese with 19 minutes remaining, Valero expertly tucking home after latching on to Persic's deflected shot.
Substitute Yann Karamoh should have piled further humiliation on Udinese late on, only for the youngster to rattle the crossbar when one-on-one with Bizzarri.
While Inter's focus is firmly on the remaining Champions League places, Udinese remain in danger of being dragged into the relegation scrap.
Key Opta Stats:
- Udinese (2D, 12L) have equalled their longest winless run in Serie A (14 games, recorded in 1951 and also in 2006).
- They have conceded at least two goals in each of their last 13 league games.
- Ten of Andrea Ranocchia's 12 Serie A goals have been scored with his head.