Milan also have a game in hand meaning they could potentially draw level with the four-in-a-row champions if they were to win next weekend's crunch clash.
Playing the league's basement sitters, Milan hardly needed a helping hand yesterday but they got exactly that as Siena goalkeeper Gianluca Curci was harshly sent off on 10 minutes.
Ronaldinho despatched the resulting penalty and Marco Borriello scored on 28 minutes to put the game to bed before half-time before the Brazilian rounded off the scoring in the second period.
Milan coach Leonardo paid tribute to his Brazilian compatriot and looked forward to the derby.
"It's normal when someone feels the love, he responds. He's entertaining everyone, he's a great player," he said of Ronaldinho.
"He's having a great season, he's rediscovered his taste for playing well and scoring goals. It's a great time in a great title race (for the derby) and it will create interest because we are closer (to Inter). There will be a lot of expectation and attention and I'm delighted to be a part of that."
Milan started in determined mood following Inter's 2-2 draw at Bari on Saturday and Ronaldinho took an Alessandro Nesta cross on his chest on three minutes before sending a spectacular overhead bicycle kick just off target.
But on 10 minutes the referee took the decision that essentially ended the game as a contest.
Jardim Brandao dithered on the ball in his own box and Borriello dispossessed him before trying to round Curci.
There was minimal contact between the pair and Borriello crumpled to the ground but the striker's last touch had been too heavy and left him no chance of reaching the ball before a back-tracking defender.
Even so, the referee pointed to the spot and showed Curci a straight red card. Substitute goalkeeper Gianluca Pegolo's first task was to pick the ball out of his net.
Siena battled on gamely and on 26 minutes Massimo Maccarone someone escaped three defenders on the edge of the Milan box to bundle through before firing over on the stretch as Thiago Silva came across to put him under pressure.
Yet just two minutes later the lead was doubled as Andrea Pirlo curled a cross into the near post and Borriello hooked a brilliant volley over his shoulder and into the top corner.
Ronaldinho proved a constant menace and had two early second half chances, flicking the ball over the bar with the first and being denied by Pegalo with the second.
But 18 minutes from time he rose unmarked in the box to head home a David Beckham corner.
Then, having tricked his way into the area Ronaldinho flicked the ball wide of the far post, but the Brazilian finally sealed his first Milan hat-trick with a rocket into the top corner from outside the area a minute from time.
Juventus slumped to their seventh defeat in 10-games with a 1-0 reverse at Chievo that is sure to increase the pressure on under-fire coach Ciro Ferrara.
Juve dropped to fifth and out of the Champions League places as both AS Roma and Napoli overtook them.
Roma moved up to third as on-loan striker Luca Toni scored his first goals for the club in a 3-0 win over free-falling Genoa.
Simone Perrotta opened the scoring on 17 minutes after a scramble at a corner and then Toni turned home Mirko Vucinic's cross on the stroke of half-time.
And on the hour mark Vucinic turned provider again for Toni to head home his second.
Napoli could not fully capitalise as they were held 0-0 at home by Palermo but still extended their unbeaten league run to 14 matches.