The full back's intervention denied Tim Cahill a second Lions goal and had the offence been seen, Clapham would have been dismissed.
Millwall could hardly have had a worse start to their campaign. Last season's play-off semi-finalists, thumped 6-0 at home on the opening day, had registered but a single point and failed to find the net in their first three outings, hardly ideal preparation for the visit of George Burley's Ipswich Town.
The Suffolk side are clear favourites for a return to the Premiership at the first attempt despite the obvious lure to their players to do so a little sooner.
Matt Holland's decision to turn down Aston Villa's approach says a lot for his personal ambitions, and Town's ability to hold on to their higher profile players shows they share that self same desire.
Life with the Lions is a little different. Manager Mark McGhee is at a loss to explain his team's poor early form but there is little doubt that the loss of Republic of Ireland winger Steven Reid and striker Richard Sadlier has been decisive.
But as the hosts took the game to their visitors there was little sign of any apprehension, as Ben May opened his professional account turning in Neil Harris's cross in only the fourth minute.
Paul Ifill saw another effort beaten away before the linesman ruled out what appeared to have been a perfectly good headed second for Cahill.
May almost stole in to double his tally, while Town were restricted to long range efforts.
Andy Marshall palmed away a Harris header while opposite number Tony Warner tipped over Marcus Bent's powerful header. After the restart, May's header against the post began the passage of play that saw Clapham go unpunished. And Darren Bent rubbed salt into the Lions wounds as he blasted a shot past Warner to equalise.
Town rallied and Darren Ambrose brought the best from Warner, but it was Millwall who finished the stronger, Andy Roberts going close and Baines again waving away loud penalty appeals as substitute Steve Claridge's shot was blocked