Ten-man Coventry City left Priestfield feeling hard done by in a dramatic clash with Gillingham which saw four penalties and a red card.
The home side were given an early platform when Dan Seaborne saw red for a foul on Cody McDonald leaving Adebayo Akinfenwa to tuck away the first of his two penalties.
Callum Wilson netted his 18th of the season from the spot just after the break although Myles Weston restored the Gills lead shortly after.
Akinfenway tucked away his second spot kick to give the hosts some breathing space but another penalty won by Wilson and converted by Baker set up a tense finish which saw Jake Hessenthaler net a 40-yard fourth for Peter Taylor's men to kill off any chance of a comeback which the Sky Blues deserved after a valiant performance despite being a man down for much of the game.
City appeared largely comfortable in the opening exchanges but McDonald turned Seaborne after 22 minutes and was then brought down by the centre half who was given his marching orders by referee Darren Sheldrake after he consulted his assistant.
Akinfenwa then stroked home the spot kick to give the Gills a half time advantage.
Sky Blues boss Steven Pressleyt rang two changes to the side that lost 2-1 at Colchester on Saturday, bringing in Nathan Delfouneso and Franck Moussa in plavce of Blair Adams and the absent Chuba Akpom.
City started the game brightly with plenty of energy and urgency and they very nearly went ahead after five minutes when Moussa got to the byline and chipped a delicate cross into the box which nearly crept inside the far post but rested on top of the goal.
Gillingham had a chance of their own on 19 minutes after an opening period of tussles between the two sides when Leon Legge headed over the bar from a corner.
Callum Wilson nearly steered in an opener two minutes later when he stretched to reach a looping ball from John Fleck and tried to lift a finish over Stuart Nelson but also lifted the ball over the bar.
Proceedings took an unwelcome turn for City after 22 minutes though when they found themselves down to ten men. Cody McDonald turned Dan Seaborne in the box but was brought down by the defender with referee Darren Sheldrake pointing to the spot and also giving Seaborne a straight red card after consulting with his assistant.
Akinfenwa then stepped up to take the penalty, sending Joe Murphy the wrong way to give the hosts the lead.
Proceedings swung the other way just three minutes after the break though in similar fashion when the Sky Blues restored parity from the spot themselves.
A ball down the left flank from Fleck found Wilson who charged into the box and was brought down by Legge, the referee pointing to the spot and Wilson dusting himself off to hammer the penalty home confidently.
The level pegging lasted just six minutes though as Gillingham restored their lead via Myles Weston. A corner delivery got a flick on from Lee which found Weston to loop a header over Joe Murphy and just under his bar.
The disappointment did not dampen City's spirt though and they were still responsible for the majority of the attacking play as the game crept over the hour mark.
The endeavour was evident when Wilson won a free kick on the left side after 62 minutes and Clarke tried to curl it inside the near post only to be denied by an equally good stop from Nelson who had to produce a diving punch to keep the ball out of the net.
Gillingham widened their lead after 73 minutes though again from the spot.
A ball cut back for Akinfenwa saw the striker shoot, only to be denied by a great save from Murphy but the assistant flagged for an infringement by Andy Webster which resulted in the referee pointing to the spot for a third time, Akinfenwa again converting.
City refused to give up though and nearly grabbed one back straight away when Wilson raced through and was only denied by a fine leg save from Nelson.
The Sky Blues got the goal their endeavour deserved with nine minutes to go though when referee Darren Sheldrake awarded a fourth spot kick.
Wilson continued to cause trouble for the Gillingham back four and raced between Legge and Joe Martin before Legge brought him down. Substiture Carl Baker then left little doubt and hammered into the top corner to set up a tense final few minutes.
Any hopes of a dramatic late comeback were effectively put to bed two minutes before the end though. Joe Murphy came high up the pitch to deal with a long ball but could not get enough on his clearance which fell to Hessenthaler who punted an effort more than 40 yards which clipped the underside of the bar in an open goal to kill off City's hopes of a result regardless of how much they deserved it.
Attendance: 5,447 (268 Sky Blue Army)
Coventry City: Murphy, Webster, Seaborne (c), Willis, Clarke, Fleck, Thomas, Moussa, Petrasso (Adams 26), Wilson, Delfouneso (Baker 68)
Subs: Burge (GK), Christie, McGeouch, Barton, Marshall
Gillingham: Nelson, Martin, Legge, Akinfenwa (Fagan 76), McDonald, Weston, Gregory, Lee (Linganzi 68), Barrett (c), Hewitt, Hessenthaler
Subs: Baxter (GK), Davies, Dack, Borrowdale, Pigott