The on-loan striker followed up Richard Garcia's stunning strike with a near-post header early in the second half and then converted a penalty with 11 minutes remaining to earn 10-man Hammers a point after young debutant Chris Cohen had been harshly sent-off for two bookable offences.
Unfortunately, Roger Cross's men were denied the three points their attacking play deserved as Coventry took advantage of some defensive errors to hit their own treble.
After making the better start, the visitors took the lead in the 12th minute, but Hammers drew level on the half hour when Garcia raced on to an exquisite pass from Daryl McMahon and, as the Coventry keeper rushed out, superbly lobbed the ball into the net from 30 yards out.
After finishing the half strongly, the hosts took the lead soon after the break. A well-worked free-kick routine saw David Noble pick out Mellor, who headed home his first goal in Hammers colours.
At that stage, Hammers were firmly on top, but the Sky Blues equalised against the run of play in the 59th minute, as a Coventry striker was left unmarked from a free-kick and headed past Stephen Bywater.
Things got worse eight minutes later when 16-year-old left-back Cohen, who travelled with the first team squad to Ipswich on Saturday, was given his marching orders for two bookable offences, although most present felt that he had been harshly punished for the tackle that brought the red card.
Soon after, another defensive mistake allowed Coventry to take the lead and seemingly secure a victory with their one-man advantage for the remainder of the game.
However, Hammers kept battling away and got their reward in the 79th minute when Mellor was fouled as he skipped into the penalty area on the right. The Liverpool man stepped up to coolly slot home the equaliser and make it two draws in two home games this season.
Roger Cross was left with mixed emotions afterwards, having seen his team excel in the attacking third but gift Coventry two goals at the other end.
"It was an exciting game," said the Hammers coach, "and there were plenty of positives to take from the evening.
"Neil Mellor scored his first two goals for the club - one of which came from a rehearsed free-kick that we had worked on this morning, something that is always pleasing - and Richard Garcia scored a fantastic first goal, so I was delighted with our attacking play.
"Sadly, we let ourselves down a bit at the other end and conceded some poor goals. Coventry had some experienced players on show, including Craig Burley and Safri, the Moroccan international, but the goals they scored were really gifted to them.
"Saying that, we had some very young players out there - the back four were all under the age of 18, with Anton Ferdinand the oldest - and they will learn from their mistakes. It was also disappointing to see young Chris Cohen sent off, I was nearby when he made the tackle and I thought he played the ball before the man, but it is one we will have to look at again.
"Shaun Byrne had to go to left-back, and he did well despite the fact he was struggling with an ankle injury. To be honest, he shouldn't really have played, but he really wanted to play and that attitude rubbed off on the other players.
"Overall, I was pleased with the effort we showed and the character and determination to come back when we went down to 10 men, but it is always disappointing to concede poor goals and it is something we need to work on."
Team: Bywater, McClenahan, Ferdinand, Blewitt, Cohen, Cole (M Noble 46), D Noble, Byrne, McMahon, Garcia, Mellor.