Yes, it is a cliché and yes you should probably avoid it. Even if you think it has happened in real life.
In a way, it is implausible if they are BEST friends, that implies they have known each other a fairly long time, and therefore if they were sexually compatible in the first place, they probably would have explored that already. To make it happen they would have to already have the sexual attraction, and be prohibited from acting on it for some reason. One is in a committed relationship, or perhaps their love is forbidden (homosexual, or crosses social or cultural boundaries; e.g. a workplace friendship, a military friendship between an officer and a non-officer). In such cases, unrequited sexual attraction might be acted upon when the situation changes, due to a change of status, place, etc.
Fairly new friendships, say within a year, can develop into love; it is not unusual for sexual attraction to be not acted upon for that long, and sometimes sexual relationships begun in mutual lust can develop overtime into love.
But psychologically speaking, best friends that know each other well are unlikely to choose to change into lovers; if it was going to happen, it would have already happened, because they have had plenty of opportunity to find something they romantically love in the other person, and would have felt sexually attracted to them and likely broached the subject already. Romantic love demands physical attraction. Love for siblings, parents, friends, children does not, but that is not what we call "falling in love." And physical attraction, although it does not have to be instantaneous, occurs fairly quickly after meeting and interacting with someone, and we expect it to either happen soon or never. It is not the kind of thing that occurs years after you've known someone (unless those years were as children).
If you want them to fall in love, I'd make them more like classmates or coworkers that have previously had little contact with each other, and the detective story ties them together on an adventure, where they get to know each other and because of that fall in love.